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Six students - 3 boys and 3 girls - are to sit side by...

by BTGmoderatorLU » Wed Jan 17, 2018 12:17 pm
Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?

A) 12
B) 36
C) 72
D) 240
E) 720

The OA si C.

I'm confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
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boys and girls

by GMATGuruNY » Wed Jan 17, 2018 1:23 pm
LUANDATO wrote:Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?

A) 12
B) 36
C) 72
D) 240
E) 720
The boys and girls must ALTERNATE.

Case 1: BGBGBG
Within the 3 red positions, the number of ways to arrange the 3 boys = 3! = 6.
Within the 3 blue positions, the number of ways to arrange the 3 girls = 3! = 6.
To combine the 6 options for the boys with the 6 options for the girls, we multiply:
6*6 = 36.

Case 2: GBGBGB
Case 2 will yield the same number of ways as Case 1:
36.

Total ways = Case 1 + Case 2 = 36+36 = 72.

The correct answer is C.
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by DrMaths » Wed Jan 17, 2018 3:22 pm
The 3 interspersed boys have 6 arrangements (ABC, ACB, BAC, BCA, CAB, CBA)
as do the girls. Also it could be boys first or girls first = 2 variations.
So 6 x 6 x 2 = 72.
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by Scott@TargetTestPrep » Sat Jan 20, 2018 6:27 am
LUANDATO wrote:Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?

A) 12
B) 36
C) 72
D) 240
E) 720
Since no two boys and no two girls can sit next to one another we can have the following arrangements:

B-G-B-G-B-G or G-B-G-B-G-B

We see that either arrangement can be selected in the following ways:

We have 3 options for the first boy, then 3 options for the first girl, then 2 options for a boy, 2 options for a girl, and then finally 1 option for each boy and girl.

This can be done in 3 x 3 x 2 x 2 x 1 x 1 = 36 ways.

Since the second arrangement can also be done in 36 ways, there are 36 + 36 = 72 possible ways of making the arrangement of no two boys and no two girls sitting next to one another.

Answer: C

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