The number of ways in which $3$ boys and $4$ girls can be seated around a circular table if no two boys 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

If $3$ sisters and $8$ other girls are together playing a game,then the number of ways in which all the girls are seated around a circle such that the three sisters are not seated together,is

In how many ways can $12$ gentlemen sit around a round table so that three specified gentlemen are always together?

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?

In how many ways can $6$ men and $5$ women be seated around a circular table if no two women are to be seated together?