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

If $5$ red roses and $5$ white roses of different sizes are used in preparing a garland,the probability that red and white roses come alternately is

If $3$ sisters and $8$ other girls are together playing a game,then the number of ways in which all the girls are seated around a circle such that the three sisters are not seated together,is

In how many ways can $12$ gentlemen sit around a round table so that three specified gentlemen are always together?

The number of ways in which $6$ men and $5$ women can sit at a round table,if no two women 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