Question: a committee of 5 people must be selected from 5 men and 8 women. 13 people in ALL. How many ways can a selection be done if there are at least 3 women on the committee? Solution: There are three cases: 1. 3 women and two men C(5,2)*C(8,3)=560 ways 2. 4 women and 1 man: C(5,1)*C(8,4)=350 ways 3. 5 women and no men: C(5,0)*C(8,5)=56 ways Total=560+350+56=966 ways. Following is the incorrect way to solve the problem: Choose 3 women and two more from the rest: C(8,3)*C(10,2)=2520 >>966 This way, we're overcounting, since some of the women chosen out of the remaining 10 could have been counted already, for example, ABC were chosen first, and G was chosen next. But then it would be the same if ABG was chosen first, and C was chosen later.
Answer: The number of possible committees is 8C5 = 8! / (5! x 3!) = (8 x 7 x 6) / (3 x 2) = 56 x 6 / 6 = 56.
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A committee of 5 people is to be selected from 8 people. How many diff [#permalink]
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Question Stats: Hide Show timer StatisticsA committee of 5 people is to be selected from 8 people. How many different committees are possible?A. 28B. 40C. 56D.168 E. 336 _________________
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Re: A committee of 5 people is to be selected from 8 people. How many diff [#permalink]
Bunuel wrote: A committee of 5 people is to be selected from 8 people. How many different committees are possible?A. 28B. 40C. 56D.168 E. 336 8C5 = 8C3 = 8 * 7 * 6 / 3! = 8 * 7 = 56.Ans: C _________________
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Re: A committee of 5 people is to be selected from 8 people. How many diff [#permalink]
Bunuel wrote: A committee of 5 people is to be selected from 8 people. How many different committees are possible?A. 28B. 40C. 56D.168 E. 336 The number of possible committees is 8C5 = 8! / (5! x 3!) = (8 x 7 x 6) / (3 x 2) = 56 x 6 / 6 = 56.Answer: C _________________
Re: A committee of 5 people is to be selected from 8 people. How many diff [#permalink] 08 Feb 2020, 12:29 |
How many ways can a committee of 5 men be formed from 8 people?
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