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There are 11 women and 9 men in a committee

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There are 11 women and 9 men in a committee [#permalink] New post 29 Sep 2005, 06:23
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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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 [#permalink] New post 29 Sep 2005, 06:36
This is a multiple step combination problem so
11!/2!9! x 9!/2!7!= 1980
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 [#permalink] New post 29 Sep 2005, 06:46
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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 [#permalink] New post 29 Sep 2005, 08:26
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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 [#permalink] New post 29 Sep 2005, 22:03
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
  [#permalink] 29 Sep 2005, 22:03
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