Question

In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together?

Answer 1

First, we seat the 5 girls in 5! ways. For each such a arrangement, the three boys can be seated only at the ‘6’ cross marks places x G x G x G x G x G x Three boys can be selected in ⁶P3 ways 

Hence total number of ways 

= 5 x ⁶P₃ = (5 x 4 x 3 x 2 x 1) x (6 x 5 x 4) = 14400