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# There are 11 women and 9 men in a committee

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Intern
Joined: 28 Jul 2005
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There are 11 women and 9 men in a committee [#permalink]

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29 Sep 2005, 07:23
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There are 11 women and 9 men in a committee. How many different groups of 4 can be formed consisting of 2 women and 2 men?

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Current Student
Joined: 29 Jan 2005
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29 Sep 2005, 07:36
This is a multiple step combination problem so
11!/2!9! x 9!/2!7!= 1980

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Senior Manager
Joined: 30 Oct 2004
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29 Sep 2005, 07:46
I think...

2 W/M from 11/9 can be selected in 11C2*9C2 = 1980 ways
For the Group of 4, The 2 W/F can be arranged in 4C2*4C2 = 36 ways.
Different groups formed will be = 1980*36 = 71280
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-Vikram

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VP
Joined: 22 Aug 2005
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29 Sep 2005, 09:26
vikramm wrote:
I think...

2 W/M from 11/9 can be selected in 11C2*9C2 = 1980 ways
For the Group of 4, The 2 W/F can be arranged in 4C2*4C2 = 36 ways.
Different groups formed will be = 1980*36 = 71280

we dont need to rearrange 4 people two TWO groups of 2 person each.do we?
you right. 11C2 * 9C2 = 1980.

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Manager
Joined: 03 Aug 2005
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29 Sep 2005, 23:03
I also go for C(11,2)*C(9,2)

You do not need to arrange the groups of four, because no matter how you arrange it, it is still the same group.
Besides, if you were to arrange the groups of four, thay could be arranged in 4! different ways

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29 Sep 2005, 23:03
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# There are 11 women and 9 men in a committee

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