Question

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?

Answer 1

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.