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

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

The number of ways in which $5$ boys and $4$ girls can sit around a circular table such that no two girls sit together is:

The number of ways in which $8$ different pearls can be arranged to form a necklace 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

The number of ways in which $6$ men and $4$ women can be seated around a table so that a particular man and a particular woman never sit adjacent to each other is