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A committee is to be created from some employees at Bongo Industrials. The committee must include exactly 3 senior

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A committee is to be created from some employees at Bongo Industrials. The committee must include exactly 3 senior

by BTGmoderatorDC » Tue Sep 28, 2021 7:37 pm

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A committee is to be created from some employees at Bongo Industrials. The committee must include exactly 3 senior executives and 4 junior executives. If 5 senior executives and 6 junior executives are available for the committee, how many different committees are possible?

A. 10
B. 15
C. 25
D. 60
E. 150



OA E

Source: Princeton Review
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Re: A committee is to be created from some employees at Bongo Industrials. The committee must include exactly 3 senior

by Brent@GMATPrepNow » Wed Sep 29, 2021 5:32 am
BTGmoderatorDC wrote: ↑
Tue Sep 28, 2021 7:37 pm
 A committee is to be created from some employees at Bongo Industrials. The committee must include exactly 3 senior executives and 4 junior executives. If 5 senior executives and 6 junior executives are available for the committee, how many different committees are possible?

A. 10
B. 15
C. 25
D. 60
E. 150



OA E

Source: Princeton Review
Take the task of creating the committee and break it into stages.

Stage 1: Select 3 senior executives to be on the committee
Since the order in which we select the 3 senior executives does not matter, we can use combinations.
We can select 3 senior executives from 5 senior executives in 5C3 ways (10 ways)
So, we can complete stage 1 in 10 ways

Stage 2: Select 4 junior executives to be on the committee
Since the order in which we select the 4 junior executives does not matter, we can use combinations.
We can select 4 junior executives from 6 junior executives in 6C4 ways (15 ways)
So, we can complete stage 2 in 15 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create the committee) in (10)(15) ways (= 150 ways)

Answer: E

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this video: https://www.gmatprepnow.com/module/gmat- ... /video/775

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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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