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

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

If $3$ sisters and $8$ brothers are together playing a game,then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the $3$ sisters are not seated together 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 $6$ men and $5$ women can dine at a round table if no two women are to sit together is given by

Five persons $A, B, C, D$ and $E$ are seated in a circular arrangement. If each of them is given a cap of one of the three colours red,blue and green,then the number of ways of distributing the caps such that the persons seated in adjacent seats get different coloured caps,is