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simple cominatorics problem... i think oa is wrong

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Senior Manager
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Joined: 11 Dec 2008
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GMAT 1: 760 Q49 V44
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simple cominatorics problem... i think oa is wrong [#permalink]

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New post 06 Aug 2009, 10:56
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

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

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How many ways are there to split a group of 6 boys into two groups of 3 boys each? (The order of the groups does not matter)

(C) 2008 GMAT Club - Probability and Combinations#16

* 8
* 10
* 16
* 20
* 24

I think the answer is d, but the OA says:

Because the groups are not ordered, we must use formula \(\frac{C_6^3}{2} = \frac{\frac{6!}{3!3!}}{2} = 10\) . We have to divide \(C_6^3\) by 2 because we need to select one group of 3 boys and the other group will be automatically selected. In other words, the three boys left after selecting of 3 from 6 will constitute the other group of 3. That's why we need to consider only the half of instances of \(C_6^3\) .


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Senior Manager
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Re: simple cominatorics problem... i think oa is wrong [#permalink]

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New post 06 Aug 2009, 13:34
order of group doesn't matter as if you choose A B C for the first group, then it's the same as choosing DEF for the 1st group....thus the (6C3)/2..great find.
Senior Manager
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Re: simple cominatorics problem... i think oa is wrong [#permalink]

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New post 06 Aug 2009, 14:22
i see... tricky :shock:

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Re: simple cominatorics problem... i think oa is wrong   [#permalink] 06 Aug 2009, 14:22
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