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

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Intern
Joined: 12 Mar 2004
Posts: 36
Location: Mumbai INDIA
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Kudos [?]: 2 [0], given: 0

If a committee of 3 people is to be selected from among 5 [#permalink]  09 Dec 2004, 21:16
00:00

Difficulty:

5% (low)

Question Stats:

100% (01:30) correct 0% (00:00) wrong based on 1 sessions
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
Joined: 03 Oct 2004
Posts: 42
Followers: 0

Kudos [?]: 1 [0], given: 0

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
Manager
Joined: 19 Nov 2004
Posts: 60
Followers: 1

Kudos [?]: 3 [0], given: 0

I'm not agree with KeyV

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

the right way is 5C1*8C1=40

I did my best to explain
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