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

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Intern
Joined: 15 Jun 2018
Posts: 11
Location: India
Concentration: Finance, Strategy
GPA: 3.45
WE: Asset Management (Commercial Banking)
If a club that consists of 9 women and 7 men is to select committee of  [#permalink]

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19 Sep 2018, 11:12
2
00:00

Difficulty:

15% (low)

Question Stats:

90% (01:31) correct 10% (02:32) wrong based on 48 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
Math Expert
Joined: 02 Aug 2009
Posts: 8753
Re: If a club that consists of 9 women and 7 men is to select committee of  [#permalink]

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19 Sep 2018, 23:44
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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Manager
Joined: 19 Oct 2017
Posts: 73
Location: India
GMAT 1: 710 Q50 V35
GPA: 3.6
WE: Analyst (Commercial Banking)
Re: If a club that consists of 9 women and 7 men is to select committee of  [#permalink]

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22 Sep 2018, 10:09
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.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3410
Re: If a club that consists of 9 women and 7 men is to select committee of  [#permalink]

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23 Sep 2018, 00:11

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.

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Re: If a club that consists of 9 women and 7 men is to select committee of   [#permalink] 23 Sep 2018, 00:11