In how many ways can $15$ members of a council sit along a circular table,when the Secretary is to sit on one side of the Chairman and the Deputy Secretary on the other side?

The number of ways in which $6$ boys and $5$ girls can sit at a round table,if no two girls are to sit together,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:

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

The number of different ways of preparing a garland using $6$ distinct white roses and $5$ distinct red roses such that no two red roses come together is

$A$ person invites $8$ guests to a dinner and places $5$ of them at one table and the remaining $3$ at another,both the tables being round. The number of ways in which the guests can be arranged is