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

$12$ persons are to be arranged at a round table. If two particular persons among them are not to be side by side,the total number of arrangements is

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

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

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

The number of ways of arranging all the letters of the word "$COMBINATIONS$" around a circle so that no two vowels come together is