Question

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

Answer 1

5 boys can be seated among themselves in ⁵P₅ = 5! Ways. After this arrangement, we have to arrange the three girls in such a way that in between two girls there atleast one boy.

So the possible places girls can be placed with the × symbol given below.

× B × B × B × B × B ×

∴ There are 6 places to seated by 3 girls which can be done 6P3 ways.

∴ Total number of ways = 5! × ⁶P₃

= 120 × (6 × 5 × 4)

= 120 × 120

= 14400