Question

In how many different ways can five boys and five girls from a circle such that the boys and girls alternate?

Answer 1

After fixing one girl, the remaining $4$ girls can sit in $4!$ Ways.

Since boys and girls have to alternate, there will be $5$ places, one place each for boys in between the girls. These $5$ places can be filled by $5$ boys in $5!$ Ways.

So, the required no.of ways $=5!\times 4!$

$=5\times 4\times 3\times 2\times 1\times 4\times 3\times 2\times 1$

$=2880$ ways