The number of ways in which $3$ boys and $4$ girls can be seated around a circular table if no two boys sit together is

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 $4$ girls can be seated around a round table such that $2$ special boys and a special girl never sit together is

In how many ways can $5$ boys and $5$ girls be seated around a circular table such that no two girls are together?

The number of ways that $8$ beads of different colours can be strung as a necklace is

The number of ways,in which $5$ girls and $7$ boys can be seated at a round table so that no two girls sit together,is