A 4-person task force is to be formed from the 4 men and 3

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

A 4-person task force is to be formed from the 4 men and 3

by AAPL » Sat Jul 06, 2019 12:15 pm

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A 4-person task force is to be formed from the 4 men and 3 women who work in Company G's human resources department. If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?

A. 14
B. 18
C. 35
D. 56
E. 144

OA B

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Source: Beat The GMAT — Problem Solving | Sat Jul 06, 2019 12:15 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Sun Jul 07, 2019 9:27 pm

AAPL wrote:GMAT Prep

A 4-person task force is to be formed from the 4 men and 3 women who work in Company G's human resources department. If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?

A. 14
B. 18
C. 35
D. 56
E. 144

OA B

The number of ways, 2 men can be selected out of 4 men = 4C2 = (4.3) / (1.2) = 6;
The number of ways, 2 women can be selected out of 3 women = 3C2 = 3C1 = 1; note that nCr = nC(r - 1)

Total number of ways the 4-person task force can be formed such that there are 2 men and 2 women in the task force = 6*3 = 18

The correct answer: B

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jul 11, 2019 6:53 pm

AAPL wrote:GMAT Prep

A 4-person task force is to be formed from the 4 men and 3 women who work in Company G's human resources department. If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?

A. 14
B. 18
C. 35
D. 56
E. 144

OA B

We need to select 2 men from a group of 4 men. Since order does not matter, we can use combinations.

4C2 = (4 x 3)/2! = 12/2 = 6

Similarly, the number of ways to select 2 women from 3 is:

3C2 = (3 x 2)/2! = 6/2 = 3

Finally, the number of ways we can choose 2 men from 4 and 2 women from 3 is:

4C2 x 3C2 = 6 x 3 = 18

Answer: B

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