Awli wrote:

In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24

B. 36

C. 72

D. 84

E. 96

Since 3 people will be on each side, and no two boys/two girls can sit together, on one side you will have Boy-Girl-Boy arrangement and on the other side you will have Girl-Boy-Girl arrangement.

From the 3 boys, choose 2 in 3C2 ways and a girl in 3C1 ways. Now you have split the boys and girls into BGB and GBG.

For BGB, pick a side (either chairs or stools) in 2 ways.

The girl takes the center seat and the 2 boys can be arranged around the girl in 2! ways.

On the other side, the boy sits in the center and the girls are arranged on his two sides in 2! ways.

Total arrangements = 3C2 * 3C1 * 2 * 2! * 2! = 72 ways.

Answer (C)

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Karishma

Veritas Prep GMAT Instructor

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