The number of circular permutations of $n$ different objects is

In how many ways can $5$ boys and $5$ girls be seated around a circular table such that no two girls are together?

The number of different ways of preparing a garland using $6$ distinct white roses and $5$ distinct red roses such that no two red roses come 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

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 ways,in which $5$ girls and $7$ boys can be seated at a round table so that no two girls sit together,is