Gmat_mission wrote: ↑

Wed Sep 29, 2021 8:04 am

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

Answer: 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

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent