From 6 men and 4 women a committee of 5 is to be formed. In : PS Archive
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# From 6 men and 4 women a committee of 5 is to be formed. In

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Director
Joined: 07 Jun 2004
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From 6 men and 4 women a committee of 5 is to be formed. In [#permalink]

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12 Jan 2005, 16:08
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From 6 men and 4 women a committee of 5 is to be formed. In how many ways this can be done if the committee is to include at least one woman.
Director
Joined: 21 Sep 2004
Posts: 610
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Kudos [?]: 33 [0], given: 0

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12 Jan 2005, 19:53
is it 255? or am I reading the question wrong..
VP
Joined: 18 Nov 2004
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12 Jan 2005, 20:27
Total Number of ways to select 5 ppl - Total ways to select committee of 5 men or no women

10C5 - 6C5 = 252 - 6 = 246 ways.
Senior Manager
Joined: 22 Jun 2004
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12 Jan 2005, 23:51
The number of ways you can choose 5 out of 10 members (6M + 4W) is 10C5 = 252

Ways that all the chosen 5 are men only = 6C5 = 6

The number of ways if the committee is to include at least one woman =
252 - 6 = 246

rxs0005 wrote:
From 6 men and 4 women a committee of 5 is to be formed. In how many ways this can be done if the committee is to include at least one woman.

_________________

Awaiting response,

Thnx & Rgds,
Chandra

Manager
Joined: 31 Aug 2004
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13 Jan 2005, 18:19
I got 246 too.

Total # of combination with both men & women: 10C5=252

The question asks for combination with at least 1 woman, and this is equivalent to total possible combination - the combination of zero woman.

Total # of combination with zero woman: 6C5 x 4C4 = 6 x 1 = 6

252-6=246

This sort of question always troubles me...
13 Jan 2005, 18:19
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