BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:43 pm
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
Answer:
C
Source: Kaplan
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
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
