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

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

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?

If $11$ members of a committee sit at a round table so that the President and Secretary always sit together,then the number of arrangements 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 $7$ men and $7$ women be seated around a circular table such that no two women sit together?