4 Indians, 3 Americans and 2 Britishers are to be arranged around a round table. Answer the following questions.

The number of ways arranging them is :

Case 1: All persons are distinct

For n distinct persons around a round table (rotations same), arrangements = \((n-1)!\).

Here, \(n=9\). So arrangements = \((9-1)! = 8! = \boxed{40{,}320}\).

Case 2: Persons are identical by nationality

If 4 Indians, 3 Americans, and 2 Britishers are considered identical within their groups, then

Arrangements = \[ \frac{(n-1)!}{4!\,3!\,2!} = \frac{8!}{4!\,3!\,2!} = \boxed{140}. \]