The number of ways in which $6$ men and $5$ women can dine at a round table if no two women are to sit together is given by

$A$ 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 $15$ members of a council sit along a circular table,when the Secretary is to sit on one side of the Chairman and the Deputy Secretary on the other side?

$21$ friends were invited for a party. Two round tables can accommodate $12$ and $9$ friends respectively. The number of ways of the seating arrangements of friends 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 $5$ 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: