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21 Nov 2018, 23:53
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
94% (00:55) correct
6%
(02:14)
wrong
based on 118
sessions
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From 7 boys and 4 girls, how many different committees can be selected consisting of 3 boys and 2 girls?
A. 108
B. 168
C. 210
D. 330
E. 462
A. 108
B. 168
C. 210
D. 330
E. 462
Archit3110
Major Poster
22 Nov 2018, 01:18
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Bunuel
Combinatrics used would be
7C3*4C2= 210 IMO C
22 Nov 2018, 13:44
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Bunuel
Take the task of creating the committee and break it into stages.
Stage 1: Select 3 boys to be on the committee
Since the order in which we select the boys does not matter, we can use combinations.
We can select 3 boys from 7 boys in 7C3 ways (35 ways)
So, we can complete stage 1 in 35 ways
Stage 2: Select 2 girls to be on the committee
Since the order in which we select the girls does not matter, we can use combinations.
We can select 2 girls from 4 girls in 4C2 ways (6 ways)
So, we can complete stage 2 in 6 ways
If anyone is interested, the video below shows you how to quickly calculate combinations (like 4C2) in your head.
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a committee) in (35)(6) ways (= 210 ways)
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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