In how many ways can a garland be made from exactly $10$ 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 $6$ men and $5$ women can sit at a round table,if no two women sit together,is:

$21$ friends were invited for a party. Two round tables can accommodate $12$ and $9$ friends respectively. The number of ways of the seating arrangements of friends is:

$8$ teachers and $4$ students are sitting around a circular table at random. Then,the probability that no two students sit together is:

The number of ways in which $6$ men and $5$ women can dine at a round table if no two women are to sit together is given by