In how many ways can $6$ men and $5$ women be seated around a circular table if no two women are to be seated together?

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

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

The number of ways in which $6$ men and $5$ women can sit at a round table,if no two women 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:

The number of ways of arranging $8$ men and $4$ women around a circular table such that no two women can sit together is