In how many ways can $7$ women and $7$ men be seated around a circular table such that each woman is seated next to a man?

In how many ways can $8$ beads of different colors be strung into a necklace?

In how many ways can $10$ people be seated around a circular table such that no two arrangements have the same neighbors? (Clockwise and counter-clockwise arrangements are considered the same.)

$21$ 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:

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

The number of ways in which $5$ boys and $4$ girls can sit around a circular table such that no two girls sit together is: