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

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Intern
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If a committee of 3 people is to be selected from among 5 [#permalink] New post 09 Dec 2004, 22:16
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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
Intern
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 [#permalink] New post 09 Dec 2004, 22:35
ans = 40

a) Total no of committees possible = 10C3 = 120
b) Number of committees with surely 1 couple = 80
c) therefore number of committees with no couple = 120-80=40.

working for b)

1st member can be chosen randomly ie in 10C1
2nd member must be spouse of member 1. So there is no choice ie 1C1
3rd member can be anyone from the remaining 8 ppl. ie 8C1

So no of 1 couple committees = 10 x 1 x 8 = 80

pls reveal OA
Thanks
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 [#permalink] New post 10 Dec 2004, 04:44
I'm not agree with KeyV
my answer is D=80

I think there is mistake in counting b)
when you count this way you duplicate the pairs

the right way is 5C1*8C1=40
120-40=80 the answer

:) I did my best to explain
  [#permalink] 10 Dec 2004, 04:44
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