In how many ways can $7$ men and $7$ women be seated around a circular table such that no two women sit together?

If $20$ beads of two different colors are to be arranged in a necklace such that they alternate,and there are $10$ beads of each color,then what is the number of ways to arrange them?

$A$ couple can sit with $6$ guests around a circular table. In how many ways can they sit if the couple sits in consecutive seats?

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