The number of ways in which $6$ men and $5$ women can sit at a round table,if no two women sit together,is:

If $20$ beads of two different colors are to be arranged in a necklace such that they alternate,and there are $10$ beads of each color,then what is the number of ways to arrange them?

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

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

In how many ways can $5$ men and $2$ women be seated around a circular table such that the two women do not sit together?

In how many ways can $4$ beads be selected and arranged in a necklace from $6$ distinct beads?