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# couple

Author Message
Intern
Joined: 02 Jun 2009
Posts: 22

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02 Jun 2009, 03:50
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

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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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CEO
Joined: 17 Nov 2007
Posts: 3484
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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03 Jun 2009, 12:08
D

1) $$C^5_3$$ - we choose 3 couples out of 5 couples.
2) $$(C^2_1)^3$$ - we choose one spouse for each couple.
3) total number = $$C^5_3*(C^2_1)^3 = 10*8 = 80$$
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Senior Manager
Joined: 16 Jan 2009
Posts: 339
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)

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03 Jun 2009, 13:40
80 = 5C3*(2C1)(2C1)(2C1)
IMO D
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Lahoosaher

Senior Manager
Joined: 15 Jan 2008
Posts: 263

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04 Jun 2009, 02:15
i have a slightly diff approach which is simple..

when encountered with such questions.. i deduct the unwanted ways from teh total number of ways..

in this case, the total number of ways is 10c3 =>120.

unwanted ways = 5 * 8 (5 couples * select one from rest of the group ) = 40.

answer = 120 - 40 = 80

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: couple   [#permalink] 04 Jun 2009, 02:15
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# couple

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