The number of ways in which $8$ different pearls can be arranged to form a necklace is

In how many ways can $8$ beads of different colors be strung into a necklace?

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

Six persons $A, B, C, D, E$ and $F$ are to be seated at a circular table facing towards the centre. Find the number of ways this can be done if $A$ must have either $E$ or $F$ on his immediate right and $E$ must have either $F$ or $D$ on his immediate right.

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

In how many ways can $15$ members of a council sit along a circular table,when the Secretary is to sit on one side of the Chairman and the Deputy Secretary on the other side?