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

In how many ways can $10$ people be seated around a circular table such that no two arrangements have the same neighbors? (Clockwise and counter-clockwise arrangements are considered the same.)

The number of ways in which $5$ male and $2$ female members of a committee can be seated around a round table so that the two female members are not seated together 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

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other is: