The number of ways in which $6$ men and $4$ women can be seated around a table so that a particular man and a particular woman never sit adjacent to each other 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

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

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

In how many ways can $4$ beads be selected and arranged in a necklace from $6$ distinct beads?

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