The number of ways that $8$ beads of different colours can be strung as a necklace is

$n$ gentlemen can be made to sit on a round table in how many ways?

If $3$ sisters and $8$ brothers are together playing a game,then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the $3$ sisters are not seated 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 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 $6$ men and $5$ women can sit at a round table,if no two women sit together,is: