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# In how many ways can 8 girls be divided into 4 sets of 2 ?

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Manager
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In how many ways can 8 girls be divided into 4 sets of 2 ? [#permalink]

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17 Jul 2007, 09:08
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In how many ways can 8 girls be divided into 4 sets of 2 ??
Manager
Joined: 04 Aug 2005
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17 Jul 2007, 11:11
dahcrap, thanks for the answer, but could you elaborate a bit? Unfortunately, I'm one of those people where if I don't know how to do something I really don't know how to do it and kind of need it spelled out for me.

Especially since Comb. & Perm. are really a struggle for me, I'm trying to collect as many good problems and answers as possible. Thanks!
Senior Manager
Joined: 03 Jun 2007
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17 Jul 2007, 11:36
ishcabibble wrote:
dahcrap, thanks for the answer, but could you elaborate a bit? Unfortunately, I'm one of those people where if I don't know how to do something I really don't know how to do it and kind of need it spelled out for me.

Especially since Comb. & Perm. are really a struggle for me, I'm trying to collect as many good problems and answers as possible. Thanks!

This is actually a simple question though worded in a convulted manner. Just find the number of ways to select 4 people from a group of 8. This is 8C4. Now multiply the remainder by 4C4. Now lets take another example. How many ways can we form 3 groups of 4 from a group of 12 people ?

The answer is First choose 4 for the first group from 12. This 12C4. NOW CHOOSE the second group from the remaining 8. This give 8C4. Now finally choose the 4 from the remaining 4. This 4C4

So the answer is 12C4*8C4*4C4. Got it ?
Manager
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18 Jul 2007, 00:44
The OA is 105. source: ps.zip from gmatclub forum.. Dont know how this answer came about
Senior Manager
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Re: PS : P & C Difficult Question [#permalink]

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18 Jul 2007, 00:53
ajay_gmat wrote:
In how many ways can 8 girls be divided into 4 sets of 2 ??

8 girls can be divided into 4 groups in 8!/[(8/4)!]^4 ways.

Imagine n distinct objects to be divided in p groups such that each contains (n/p) objects. This can be done in n!/[(n/p)!]^p ways.

Arrangements of the groups will not matter, hence, we have to divide the result by p!.

Thus, we have the required no. of ways = 8!/(2^4 * 4!) = 105.
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18 Jul 2007, 10:18
Thanks, dahcrap. Much appreciated!
Senior Manager
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Re: PS : P & C Difficult Question [#permalink]

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18 Jul 2007, 10:48
dahcrap wrote:
ajay_gmat wrote:
In how many ways can 8 girls be divided into 4 sets of 2 ??

8C4 * 4C4

Oh Sorry I misunderstood the question as 2 sets of 4.

In this it is 8C2*6C2*4C2*2C2*4! whch equates to sumande's 8!/2^4 * 4!
Re: PS : P & C Difficult Question   [#permalink] 18 Jul 2007, 10:48
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