Question

Find the number of ways in which $5$ boys and $5$ girls be seated in a row so that all the girls sit together and all the boys sit together.

Answer 1

The two groups of girls and boys can be arranged in $2!$ ways $5$ girls can be arranged among themselves in $5!$ Ways. Similarly, $5$ boys can be arranged among themselves in $5!$ ways. Hence, by the fundamental principle of counting, the total number of requisite seating arrangements $=2!(5!\times 5!)=2{(5!)}^2$