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

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

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

In how many ways can $8$ beads of different colors be strung into a necklace?