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

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:

$8$ teachers and $4$ students are sitting around a circular table at random. Then,the probability that no two students sit together is:

In how many ways can $7$ women and $7$ men be seated around a circular table such that each woman is seated next to a man?

Five persons $A, B, C, D$ and $E$ are seated in a circular arrangement. If each of them is given a cap of one of the three colours red,blue and green,then the number of ways of distributing the caps such that the persons seated in adjacent seats get different coloured caps,is

If $3$ sisters and $8$ brothers are together playing a game,then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the $3$ sisters are not seated together is