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If a club that consists of 9 women and 7 men is to select committee of

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Joined: 15 Jun 2018
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Concentration: Finance, Strategy
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If a club that consists of 9 women and 7 men is to select committee of  [#permalink]

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New post 19 Sep 2018, 12:12
1
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

92% (01:15) correct 8% (01:04) wrong based on 37 sessions

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If a club that consists of 9 women and 7 men is to select committee of 2 women and 3 men, how many possible different committees can be formed?

A) 360
B) 720
C) 1260
D) 1560
E) 1960
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Joined: 02 Aug 2009
Posts: 6986
Re: If a club that consists of 9 women and 7 men is to select committee of  [#permalink]

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New post 20 Sep 2018, 00:44
CaptainGMAT wrote:
If a club that consists of 9 women and 7 men is to select committee of 2 women and 3 men, how many possible different committees can be formed?

A) 360
B) 720
C) 1260
D) 1560
E) 1960


Most important info here... it is SELECTION, so a combinations question that is order does not matter

so choose 2 out of 9 women and 3 out of 7 men = \(9C2*7C3=\frac{9!}{7!2!} * \frac{7!}{4!*3!} = \frac{9*8*7*6*5}{3*2*2}=20*63=1260\)

C
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Joined: 19 Oct 2017
Posts: 47
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Re: If a club that consists of 9 women and 7 men is to select committee of  [#permalink]

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New post 22 Sep 2018, 11:09
CaptainGMAT wrote:
If a club that consists of 9 women and 7 men is to select committee of 2 women and 3 men, how many possible different committees can be formed?

A) 360
B) 720
C) 1260
D) 1560
E) 1960




9C2*7C3 = 1260. Answer is C.

Why is this tagged under probability. This should be tagged under Combinations. Moderators please do the needful. Thanks.
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Re: If a club that consists of 9 women and 7 men is to select committee of  [#permalink]

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New post 23 Sep 2018, 01:11

Solution



Given:
    • A club consists of 9 women and 7 men
    • A committee, of 2 women and 3 men, is to be selected from the club

To find:
    • Number of different committees that can be formed

Approach and Working:
From 9 women, we need to select 2 women for the committee.
    • Number of ways we can select 2 women = \(^9C_2\) = 36

From 7 men, we need to select 3 men for the committee
    • Number of ways we can select 3 men = \(^7C_3\) = 35

Therefore, the number of different committees can be formed = 36 * 35 = 1260

Hence, the correct answer is option C.

Answer: C
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