If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

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

$A$ family consisting of a mother,father,and their $8$ children ($4$ boys and $4$ girls) are to be seated at a round table in a party. How many ways can this be done if the mother and father sit together and the males and females alternate?

In how many ways can $5$ keys be arranged in a ring?

If $12$ people are to be seated around a circular table,in how many ways can they be seated such that two specific individuals do not sit together?