If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

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?

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

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

$A$ round table conference is to be held amongst $20$ countries. If two particular delegates wish to sit together,then in how many ways can such arrangements be done?

$4$ gentlemen and $4$ ladies are to be seated at a round table. What is the probability that they sit alternately?