Find the number of different garlands that can be prepared using $5$ different coloured flowers.

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

If $11$ members of a committee sit at a round table so that the President and Secretary always sit together,then the number of 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:

The number of ways in which $8$ different pearls can be arranged to form a necklace is

In how many ways can $6$ men and $5$ women be seated around a circular table if no two women are to be seated together?