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From a group of three boys and four girls, a school hallway monitor gr
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28 Sep 2021, 09:28
28 Sep 2021, 09:28
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From a group of three boys and four girls, a school hallway monitor group is to be selected. If the group is to be formed of one boy and four girls, how many different such groups can be formed?
A. 1
B. 3
C. 36
D. 72
E. 360
A. 1
B. 3
C. 36
D. 72
E. 360
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From a group of three boys and four girls, a school hallway monitor gr
[#permalink]
28 Sep 2021, 09:46
28 Sep 2021, 09:46
1
Carcass wrote:
From a group of three boys and four girls, a school hallway monitor group is to be selected. If the group is to be formed of one boy and four girls, how many different such groups can be formed?
A. 1
B. 3
C. 36
D. 72
E. 360
A. 1
B. 3
C. 36
D. 72
E. 360
Take the task of creating a hallway monitor group and break it into stages.
Stage 1: Select 4 girls to be in the group
Since there are only 4 girls to choose from, there's only 1 way to select 4 girls - you must select ALL of them, so there's only 1 way.
Alternatively, we COULD say that we can select 4 girls from the 4 girls in 4C4 ways (which also equals 1)
So, we can complete stage 1 in 1 way
Stage 2: Select 1 boy to be in the group
Since there are 3 boys to choose from, we can complete stage 2 in 3 ways
By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus create a 4-person hallway monitor group) in (1)(3) ways (= 3 ways)
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn this technique.
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From a group of three boys and four girls, a school hallway monitor gr [#permalink]
28 Sep 2021, 09:46
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