The number of ways in which $6$ boys and $5$ girls can sit at a round table,if no two girls are to sit together,is

The number of ways of arranging $2$ red,$3$ white,and $5$ yellow roses of different sizes into a garland such that no two yellow roses come together is

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

The number of ways in which $3$ boys and $4$ girls can be seated around a circular table if no two boys sit together 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:

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?