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

Five persons $A, B, C, D$ and $E$ are seated in a circular arrangement. If each of them is given a cap of one of the three colours red,blue and green,then the number of ways of distributing the caps such that the persons seated in adjacent seats get different coloured caps,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

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

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