The number of circular permutations of $n$ distinct objects is......

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

The number of ways of arranging $8$ men and $4$ women around a circular table such that no two women can sit together is

The number of ways of arranging $9$ men and $5$ women around a circular table so that no two women come together are

$A$ couple can sit with $6$ guests around a circular table. In how many ways can they sit if the couple sits in consecutive seats?

The number of ways of arranging $2$ red,$3$ white,and $5$ yellow roses of different sizes into a garland such that no two yellow roses come together is