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.

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

$A$ round table conference is to be held amongst $20$ countries. If two particular delegates wish to sit together,then in how many ways can such arrangements be done?

If $11$ members of a committee sit at a round table so that the President and Secretary always sit together,then the number of arrangements is

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

$12$ persons are to be arranged at a round table. If two particular persons among them are not to be side by side,the total number of arrangements is