In how many ways can a garland be made from exactly $10$ flowers?

The number of ways of arranging $8$ men and $4$ women around a circular table such that no two women can sit together is

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 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

$A$ person invites $8$ guests to a dinner and places $5$ of them at one table and the remaining $3$ at another,both the tables being round. The number of ways in which the guests can be arranged is

In how many ways can $7$ men and $7$ women be seated around a circular table such that no two women sit together?