The number of ways,in which $5$ girls and $7$ boys can be seated at a round table so that no two girls sit together,is

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other is:

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

$A$ 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 in which $6$ men and $5$ women can sit at a round table,if no two women sit together,is:

The number of ways that $8$ beads of different colours can be strung as a necklace is