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

The number of ways in which $5$ boys and $3$ girls can be seated on a round table,if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,is

If $12$ people are to be seated around a circular table,in how many ways can they be seated such that two specific individuals do not sit together?

The number of different ways of preparing a garland by using $6$ distinct white roses and $6$ distinct red roses such that no two red roses come together is

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 $5$ male and $2$ female members of a committee can be seated around a round table so that the two female members are not seated together is: