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:

$A$ person invites $8$ guests to a dinner and places $5$ of them at one table and the remaining $3$ at another,both the tables being round. The number of ways in which the guests can be arranged is

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

Find the number of ways in which two Americans,two British,one Chinese,one Dutch,and one Egyptian can sit at a round table so that persons of the same nationality are separated.

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

The number of ways that $8$ beads of different colours can be strung as a necklace is