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A committee of three people is to be chosen from four

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Manager
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A committee of three people is to be chosen from four [#permalink]  13 Nov 2007, 07:31
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A committee of three people is to be chosen from four 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

1. 16
2. 24
3. 26
4. 30
5. 32
Manager
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The committee could have

0 men and 3 women = 4 possibilities ( 4c3 )
1 man and 2 women = 12 possibilities ( no couple should be in the team : 4 * 3c2 )
2 men and 1 woman = 12 possibilities ( no couple should be in the team : 4c2 *2c1 )
3 men and 0 women = 4 possibilities ( 4c3 )

Therefore 4+12+12+4=32 possible teams.
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E.

N=4C3*2C1*2C1*2C1=4*2*2*2=32

4C3 - 3 couples from 4 couples
2C1 - a man or woman from a couple.
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Another way to look at this is the Manhattan GMAT technique. For a restriction problem like this you want to look at it in two parts:

Total Possible Combos - Restricted Combos.

So total possible without any restrictions is:

8!/(3!)(5!) = 56 total possibilities

Now you look at the restrictions. What is the restriction -- a couple can't be together. How many are restricted? When looking at a restriction it is best to look at them as a total unit. So 1 couple is a unit. We have four couples. How can we arrange this 4 units? 4*3*2*1 = 24 combos restricted.

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Re: PS...Probability ... prep [#permalink]  07 Sep 2009, 10:36
The same as here ps-combinatorics-m02q05-55472.html
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Manager
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Re: PS...Probability ... prep [#permalink]  28 Sep 2009, 04:11
A committee of three people is to be chosen from four 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

1. 16
2. 24
3. 26
4. 30
5. 32

Ans: 8 * 6 * 4/3!

32 ways..

Ans is option 5
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Re: PS...Probability ... prep [#permalink]  02 May 2011, 23:05
8*6*4 = total ways
3! is the number of permutations of 3 people.

hence 24*8/6 = 32
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Re: PS...Probability ... prep   [#permalink] 02 May 2011, 23:05
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