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

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Joined: 18 Apr 2015
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In how many ways can a committee of 5 members be formed from [#permalink]  14 May 2019, 00:33
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Question Stats:

83% (02:42) correct 16% (03:10) wrong based on 6 sessions
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
[Reveal] Spoiler: OA

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Manager
Joined: 22 Aug 2019
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Re: In how many ways can a committee of 5 members be formed from [#permalink]  22 Aug 2019, 19:23
1
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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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Joined: 27 Jun 2019
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Re: In how many ways can a committee of 5 members be formed from [#permalink]  27 Aug 2019, 13:23
1
KUDOS
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.
Re: In how many ways can a committee of 5 members be formed from   [#permalink] 27 Aug 2019, 13:23
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