Question

In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?

Answer 1

Total number of boys = 6
Total number of girls = 5
Now,
Five girls can sit on chairs in a row in $5_{P_5}$ = 5! ways.and 6 boys can stand behind them in a row in $6_{P_6}$ = 6! ways. Hence, the total number of ways = $5!\times 6!$
= $5\times 4\times 3\times 2\times 1\times 6\times 5\times 5\times 4\times 3\times 2\times 1$
= $120\times 720$ = 86400