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# A commitee of three people is to be chosen from four married

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Manager
Joined: 22 Feb 2006
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A commitee of three people is to be chosen from four married [#permalink]

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07 Jun 2006, 12:20
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A commitee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

A) 16
B) 24
C) 26
D) 30
E) 32
Intern
Joined: 28 Nov 2005
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08 Jun 2006, 01:48
I come up with 8*6*4=192

1)How many ways to pick 1 person out of 8 people: 8
2)How many ways to pick 1 person out of 6 (7remaining-1 the partner of the already selected one =6): 6
3)How many ways to pick 1 person out of 4 : 4

Total: 8*6*4=192 ways

Can anyone explain what's wrong with this reasoning ?
Manager
Joined: 09 May 2006
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Location: Bangalore, India
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08 Jun 2006, 02:04
TriColor wrote:
A commitee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

A) 16
B) 24
C) 26
D) 30
E) 32

Much repeated question. Good explanations on following links:

http://www.gmatclub.com/phpbb/viewtopic ... +committee

http://www.gmatclub.com/phpbb/viewtopic ... +committee
Manager
Joined: 22 Feb 2006
Posts: 96
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08 Jun 2006, 10:29
Hey Hidalgo!

I think that you need to add one more step to your calculation.

You need to divide by 3! (or K!) because we are not interested in the order of who we pick for three-member team.

Note: there are k! number of permutations for each combination! That's why we are dividing by k!.

And thanks to shobhitb and X & Y for your help too!
VP
Joined: 02 Jun 2006
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08 Jun 2006, 10:43
Number of ways to form committe of 3 members (w/o couples ) = 8 x 6x 4

As we don't care about the order we need to divide it by the factorial of the total number of members picked = 3!

Therefore, # of ways = (8x6x4)/6 =32
Manager
Joined: 25 May 2006
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08 Jun 2006, 11:09
First you calculate ALL possible combinations:

8!/(5!*3!)=56

Then you calculate possible combination where you can arrange 2 people that are married and another person. This gives you 24 possible combinations.

56-24= 32

Cheers!!
08 Jun 2006, 11:09
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