The number of circular permutations of $n$ different objects is

$n$ gentlemen can be made to sit on a round table in how many ways?

$21$ 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 $6$ men and $5$ women can sit at a round table,if no two women sit together,is:

The number of different ways of preparing a garland by using $6$ distinct white roses and $6$ distinct red roses such that no two red roses come together is

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