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# If a committee of 3 people is to be selected from among 5

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Joined: 30 Jan 2006
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If a committee of 3 people is to be selected from among 5 [#permalink]  12 Aug 2007, 11:53
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If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A. 20 B. 40 C. 50 D. 80 E. 120
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Joined: 09 Aug 2007
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total number of ways to form groups of 3 from 10 people:

10!/3!(7!) = 120

calc ways to form a committee containing one married couple by calculating number of ways to select one couple from 5 and multiplying by the number of ways to fill the third slot on this committee from the remaining 8 people:

5!/1!(4!) = 5

8!/1!(7!) = 8

5*8 = 40 ways to select a committee with one married couple.

120 - 40 = 80 ways to form a 3 person committee with no married couples.
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