Question

We must place $5$ boys and $5$ girls round the table, so that no two boys and no two girls sit side by side. In how many ways can we do it?

Answer 1

Leaving One vacant seat between two boys ,$5$ boys can be seated in $4!$ ways.

Then at remaining $5$ seats, $5$ girls can seat in $5!$ ways.

Hence total ways are $4!\times 5!$