In how many ways can $5$ keys be arranged in a ring?

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 $3$ 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

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

Six persons $A, B, C, D, E$ and $F$ are to be seated at a circular table facing towards the centre. Find the number of ways this can be done if $A$ must have either $E$ or $F$ on his immediate right and $E$ must have either $F$ or $D$ on his immediate right.

The number of ways of arranging $9$ men and $5$ women around a circular table so that no two women come together are