In how many ways can $7$ men and $7$ women be seated around a circular table such that no two women sit together?

$12$ persons are to be arranged at a round table. If two particular persons among them are not to be side by side,the total number of arrangements is

The number of ways in which $6$ men and $4$ women can be seated around a table so that a particular man and a particular woman never sit adjacent to each other is

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

$A$ couple can sit with $6$ guests around a circular table. In how many ways can they sit if the couple sits in consecutive seats?

If $11$ members of a committee sit at a round table so that the President and Secretary always sit together,then the number of arrangements is