Find the total number of ways to form a 3 digit number without repetition from the digits 0, 1,2,5

Solution: 

Answer: 125.

Method:

Here, Total number of digits = 5

Let 3-digit number be XYZ.

Now the number of digits available for X = 5,

As repetition is allowed,

So the number of digits available for Y and Z will also be 5 (each).

Thus, The total number of 3-digit numbers that can be formed = 5×5×5 = 125.

Solution:

Answer: 60.

Method:

Here, Total number of digits = 5

Let 3-digit number be XYZ.

Now the number of digits available for X = 5,

As repetition is not allowed,

So the number of digits available for Y = 4 (As one digit has already been chosen at X),

Similarly, the number of digits available for Z = 3.

Thus, The total number of 3-digit numbers that can be formed = 5×4×3 = 60.

Problem 2: How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Solution:

Answer: 108.

Method:

Here, Total number of digits = 6

Let 3-digit number be XYZ.

Now, as the number should be even so the digits at unit place must be even, so number of digits available for Z = 3 (As 2,4,6 are even digits here),

As the repetition is allowed,

So the number of digits available for X = 6,

Similarly, the number of digits available for Y = 6.

Thus, The total number of 3-digit even numbers that can be formed = 6×6×3 = 108.

Problem 3: How many 4-letter code can be formed using the first 10 letters of the English alphabet if no letter can be repeated? 

Solution:

Answer: 5040

Method:

Here, Total number of letters = 10

Let the 4-letter code be 1234.

Now, the number of letters available for 1st place = 10,

As repetition is not allowed,

So the number of letters possible at 2nd place = 9 (As one letter has already been chosen at 1st place),

Similarly, the number of letters available for 3rd place = 8,

and the number of letters available for 4th place = 7.

Thus, The total number of 4-letter code that can be formed = 10×9×8×7 = 5040.

Problem 4: How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Solution:

Answer: 336

Method:

Here, Total number of digits = 10 (from 0 to 9)

Let 5-digit number be ABCDE.

Now, As the number should start from  67 so the number of possible digits at A and B = 1 (each),

As repetition is not allowed,

So the number of digits available for C = 8 ( As 2 digits have already been chosen at A and B),

Similarly, the number of digits available for D = 7,

and the number of digits available for E = 6.

Thus, The total number of 5-digit telephone numbers that can be formed = 1×1×8×7×6 = 336.

Problem 5: A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Solution:

Answer: 8

Method:

We know that, the possible outcome after tossing a coin is either head or tail (2 outcomes),

Here, a coin is tossed 3 times and outcomes are recorded after each toss,

Thus, the total number of outcomes = 2×2×2 = 8.

Problem 6: Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

Solution:

Answer: 20.

Method:

Here, Total number of flags = 5

As each signal requires 2 flag and signals should be different so repetition will not be allowed,

So, the number of flags possible for the upper place = 5,

and the number of flags possible for the lower place = 4.

Thus, the total number of different signals that can be generated = 5×4 = 20.

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Q.

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3-digit numbers can be formed using the digit 0, 1, 2, 3 without repetitions?

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

Evaluate

(a) 5!

(b) 2! + 1! + 0!

(c) 5P3

Find the number of permutations of the letters of the words

(a) MILK (b) WORLD

If nP4 = 12 nP2 the find n.

Find r if : (a) 13Pr = 156 (b) 8Pr = 336

How many 3 digit numbers can be formed using the digit 2, 3, 4, 5 and 6 without repetitions? How many of these are even numbers?

Q.

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

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Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3-digit numbers can be formed using the digit 0, 1, 2, 3 without repetitions?

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

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Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

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We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

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We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

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We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

Evaluate

(a) 5!

(b) 2! + 1! + 0!

(c) 5P3

Find the number of permutations of the letters of the words

(a) MILK (b) WORLD

If nP4 = 12 nP2 the find n.

Find r if : (a) 13Pr = 156 (b) 8Pr = 336

How many 3 digit numbers can be formed using the digit 2, 3, 4, 5 and 6 without repetitions? How many of these are even numbers?

Q.

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

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Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

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Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3-digit numbers can be formed using the digit 0, 1, 2, 3 without repetitions?

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

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We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

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How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

Evaluate

(a) 5!

(b) 2! + 1! + 0!

(c) 5P3

Find the number of permutations of the letters of the words

(a) MILK (b) WORLD

If nP4 = 12 nP2 the find n.

Find r if : (a) 13Pr = 156 (b) 8Pr = 336

How many 3 digit numbers can be formed using the digit 2, 3, 4, 5 and 6 without repetitions? How many of these are even numbers?

Q.

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

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Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

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Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

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Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3-digit numbers can be formed using the digit 0, 1, 2, 3 without repetitions?

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

Evaluate

(a) 5!

(b) 2! + 1! + 0!

(c) 5P3

Find the number of permutations of the letters of the words

(a) MILK (b) WORLD

If nP4 = 12 nP2 the find n.

Find r if : (a) 13Pr = 156 (b) 8Pr = 336

How many 3 digit numbers can be formed using the digit 2, 3, 4, 5 and 6 without repetitions? How many of these are even numbers?

Q.

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3-digit numbers can be formed using the digit 0, 1, 2, 3 without repetitions?

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

How many 3 digit numbers can be formed using the digit 0,1,2,3 without repetitions?

The four given digits are 0, 1, 2 and 3.

Three-digit numbers are of the form

We need to find the number of 3-digit numbers that can be formed using the given digits without repetition.

0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3).

Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits.

Thus, there are

Evaluate

(a) 5!

(b) 2! + 1! + 0!

(c) 5P3

Find the number of permutations of the letters of the words

(a) MILK (b) WORLD

If nP4 = 12 nP2 the find n.

Find r if : (a) 13Pr = 156 (b) 8Pr = 336

How many 3 digit numbers can be formed using the digit 2, 3, 4, 5 and 6 without repetitions? How many of these are even numbers?