From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Apr 15, 2020 5:47 pm

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From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

OA C

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Wed Apr 15, 2020 5:47 pm

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

Re: From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly

by Jay@ManhattanReview » Thu Apr 16, 2020 12:32 am

BTGmoderatorDC wrote: ↑
Wed Apr 15, 2020 5:47 pm
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

OA C

Source: Magoosh

The no. of committees that have exactly 2 boys and 2 girls = 5C2*4C2 = 60

The correct answer: C

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly

by Scott@TargetTestPrep » Sun Apr 19, 2020 4:08 am

BTGmoderatorDC wrote: ↑
Wed Apr 15, 2020 5:47 pm
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

OA C

Source: Magoosh

We can select 2 girls in 4C2 = (4 x 3)/2! = 6 ways.

We can select 2 boys in 5C2 = (5 x 4)/2! = 10 ways.

Thus, the group can be formed in a total of 6 x 10 = 60 ways.

Answer: C

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