In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

The number of ways in which $6$ boys and $5$ girls can sit at a round table,if no two girls are to sit together,is

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

Five boys and five girls are to be seated around a circular table. The number of ways in which they can be seated such that no two boys and no two girls are together is:

$12$ persons are to be arranged at a round table. If two particular persons among them are not to be side by side,the total number of arrangements is

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