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

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

The number of ways of arranging $8$ men and $4$ women around a circular table such that no two women can sit together is

If $A$ and $B$ are among $20$ persons who sit at random along a round table,then the probability that there are exactly six persons between $A$ and $B$ is

The number of ways in which $5$ beads of different colours form a necklace 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