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:

Find the number of different garlands that can be prepared using $5$ different coloured flowers.

The number of ways in which $5$ boys and $4$ girls can sit around a circular table such that no two girls sit together is:

The number of different ways of preparing a garland by using $6$ distinct white roses and $6$ distinct red roses such that no two red roses come together is

Let $m$ denote the number of ways in which $5$ boys and $5$ girls can be arranged in a line alternately,and $n$ denote the number of ways in which $5$ boys and $5$ girls can be arranged in a circle so that no two boys are together. If $m = kn$,then the value of $k$ 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?