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

If $5$ red roses and $5$ white roses of different sizes are used in preparing a garland,the probability that red and white roses come alternately 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

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

The number of ways of arranging $8$ men and $4$ women around a circular table such that no two women can sit together is