Question

Find the number of ways in which 5 boys and 5 girls be seated in a row so that no two girls may sit together.

Answer 1

$5$ boys can be seated in a row in ${}^5{P}_5$ ways.

Now, in the $6$ gaps $5$ girls can be arranged in ${}^6{P}_5$ ways.

Hence, the number of ways in which no two girls sit together $=5!{\times }^6{P}_5=5!\times 6!$