4 boys and 3 girls are to be seated in 7 chairs such that no two boys are together. In how many ways can this be done?

1 Answer
MathFact-orials.blogspot.com
Aug 3, 2018

144

Explanation:

Notice that the only way to have two boys not sitting next to each other requires that the seating be:

B G B G B G B

There are #4! = 24# ways to sit the boys in the boy seats and #3! = 6# ways to sit the girls in the girl seats. This gives:

#24xx6=144# ways the boys and girls can sit.

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