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In how many ways can 10 similar chocolates be distributed among 4 children of different ages such that each child gets, at least, one chocolate.a)13C3b)10C4c)9C3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for CAT 2022 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In how many ways can 10 similar chocolates be distributed among 4 children of different ages such that each child gets, at least, one chocolate.a)13C3b)10C4c)9C3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2022 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways can 10 similar chocolates be distributed among 4 children of different ages such that each child gets, at least, one chocolate.a)13C3b)10C4c)9C3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
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In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
Awamy wrote:
why the formula of identical objects doen'st work here ?
Is there any easy way to solve such problems please ?
So in this question, since 6 identical chocolates have to be distributed among 3 distinct people, but everyone should get at least one, we will apply the second formula = (6-1) C (3-1) = 5C2 = 10, which is our answer
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56
SOURCE: //www.GMATinsight.com
Hi# of chocolates distributed to each child -\(x_1, x_2, x_3\), where \(x_i > 0\)We have non-empty set:\(x_1 + x_2 + x_3 = 6\)We need to convert it into \(x_i >=0\) substituting each \(x_i\) with \(y_i = x_i - 1\). \(x_i = y_i +1\):\(y_1 + y_2 + y_3 = 3\)\(_{3+3-1}C_3 = _5C_3 = \frac{5*4}{2} = 10\)Answer A
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56
SOURCE: //www.GMATinsight.com
\\since a child must get at least 1 chocolate, lets distribute 1 chocolate to each child first, and thus we are left with 3 chocolates to redistribute now we are in businesssince chocolates are identical, the remaining 3 chocolates can be distributed among 3 children as follows 5!_____3! 2!= 10, the answer hope this helpsthankscheers, and do consider some kudos, guys
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
why the formula of identical objects doen'st work here ?
Is there any easy way to solve such problems please ?
Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
chetan2u Bunuel could you please explain how to solve this without (n-1)Cr-1 ... i wanna learn the concept
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56
SOURCE: //www.GMATinsight.com
formula to use here we can take case that child may get 0 chocolate n-1Cr-1 ; n=6 . r= 3 5c2; 10IMO A
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56
SOURCE: //www.GMATinsight.com
given: 6 identical chocs, 3 different kids, at least 1 each;\(k_1+k_2+k_3=6…(k_1'+1)+(k_2+1)+(k_3+1)=6…k_1'+k_2+k_3=3\)\(C(n+r-1,r-1)=(3+3-1,3-1)=\frac{5!}{2!3!}=10\)Answer (A)
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56
SOURCE: //www.GMATinsight.com
The detailed solution to the above problem using two methods is explained in the attached video
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56
SOURCE: //www.GMATinsight.com
Let the children be A, B, and C. So A can get 1, B can get 1 and C can get 4 chocolates. Of course, this is different from A gets 4, B 1, and C 1, or, A gets 1, B 4, and C 1. In the calculations below, we will show how 3 positive integers can sum to 6 and the number of ways the 3 numbers can be rearranged among A, B, and C (for example, the first calculation below describes the distribution of the 6 chocolates mentioned above): 1 + 1 + 4 = 63!/2! = 3 ways1 + 2 + 3 = 6 3! = 6 ways2 + 2 + 2 = 63!/3! = 1 wayTherefore, there are a total of 3 + 6 + 1 = 10 ways that 6 chocolates can be distributed to 3 children._________________
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
22 Jan 2022, 09:50