The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other is:

The number of ways in which $5$ boys and $4$ girls can sit around a circular table such that no two girls 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 that $8$ beads of different colours can be strung as a necklace is

The number of ways of arranging $2$ red,$3$ white,and $5$ yellow roses of different sizes into a garland such that no two yellow roses come together is

In how many ways can a garland be made from exactly $10$ flowers?