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In how many ways can a committee of 5 members be formed from

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In how many ways can a committee of 5 members be formed from [#permalink] New post   14 May 2019, 00:33
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In how many ways can a committee of 5 members be formed from 4 women and 6 men such that at least 1 woman is a member of the committee?

(A) 112

(B) 156

(C) 208

(D) 246

(E) 252
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Re: In how many ways can a committee of 5 members be formed from [#permalink] New post   22 Aug 2019, 19:23
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Carcass wrote:
In how many ways can a committee of 5 members be formed from 4 women and 6 men such that at least 1 woman is a member of the committee?

(A) 112

(B) 156

(C) 208

(D) 246

(E) 252


Because the committee needs to consist of 5 people:
Choose one girl and 4 dudes,
choose 2 girls and 3 dudes,
etc....

4C1 * 6C4 +
4C2 * 6C3 +
4C3 * 6C2 +
4C4 * 6C1 =
246

So D.
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Re: In how many ways can a committee of 5 members be formed from [#permalink] New post   27 Aug 2019, 13:23
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Carcass wrote:
In how many ways can a committee of 5 members be formed from 4 women and 6 men such that at least 1 woman is a member of the committee?

(A) 112

(B) 156

(C) 208

(D) 246

(E) 252


There are 10C5 = 252 ways to pick a 5 member committee out of 10 people (this includes committees with at least one woman and committees with no women at all). To get the number of committees with at least one woman, we should subtract the number of committees with no women from the total number of possible committees. There are 6C5 = 6 ways to pick the 5 member committee from men only. Thus, the number of committees where at least 1 woman is a member = 252 - 6 = 246. Answer D.
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Re: In how many ways can a committee of 5 members be formed from [#permalink] New post   19 Jun 2024, 04:54
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Re: In how many ways can a committee of 5 members be formed from [#permalink]
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