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

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

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 $6$ men and $4$ women can be seated around a table so that a particular man and a particular woman never sit adjacent to each other is

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