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

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

The number of ways of arranging $2$ red,$3$ white,and $5$ yellow roses of different sizes into a garland such that no two yellow roses come together 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

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 in which $5$ boys and $4$ girls can sit around a circular table such that no two girls sit together is: