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# How many different ways can a group of 12 people be divided

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CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City
How many different ways can a group of 12 people be divided [#permalink]

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12 Dec 2007, 06:28
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many different ways can a group of 12 people be divided into 6 different teams of 2 people each?
Director
Joined: 12 Jul 2007
Posts: 858

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12 Dec 2007, 07:14
would it be...

(12*11)+(10*9)+(8*7)+(6*5)+(4*3)+(2*1)

132+90+56+30+12+2 = 322 ways

I'm not 100% confident with that answer. What's the OA?
CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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12 Dec 2007, 08:09
N=12C2*10C2*8C2*6C2*4C2*2C2/6!=10395

http://www.gmatclub.com/forum/t55369
CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

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12 Dec 2007, 08:33
There are going to be 6 groups. 6!

11 * 9 * 7 * 5 * 3
99 * 35 * 3
10,395

This is a variant q i made up.
Director
Joined: 12 Jul 2007
Posts: 858

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12 Dec 2007, 09:04
bmwhype2 wrote:
There are going to be 6 groups. 6!

11 * 9 * 7 * 5 * 3
99 * 35 * 3
10,395

This is a variant q i made up.

Is this the thought process here.

You have 12 people being split up into 6 groups and order doesn't matter (Joe and Susie = Susie + Joe)

It doesn't matter who you choose first, you have 11 choices from their partner.

Then it doesn't matter who you choose next, but you have 9 people to team up with them

etc etc

I like that way. Very simple and straight forward
12 Dec 2007, 09:04
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# How many different ways can a group of 12 people be divided

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