Find the number of ways of seating 5 Indians, 4 Americans and 3 Russians at a round table so that
no two Russians sit together

Explanation

First we arrange the 5 Indians +4 Americans around the table in (9-1) ! =8! Ways.
Now, we can find 9 gaps in between these 9 persons (one gap between any two consecutive persons).
The 3 Russians can be arranged in the 9 gaps in `""^(9)P_(3)` ways. Hence, the number of required arrangements is `8!xx""^(9)P_(3)`.