The number of circular permutations of $n$ different objects 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

Let $m$ denote the number of ways in which $5$ boys and $5$ girls can be arranged in a line alternately,and $n$ denote the number of ways in which $5$ boys and $5$ girls can be arranged in a circle so that no two boys are together. If $m = kn$,then the value of $k$ is

In how many ways can $5$ keys be put in a ring?

If $n$ persons are seated around a circular table,what is the ratio of the unfavorable probability to the favorable probability that two specific persons sit together?

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