Explanation
1. Grouping the Americans
Since the 3 Americans must sit together, we treat them as a single unit (or one block).
-
Remaining people: 4 Indians + 2 Britishers = 6 individuals.
-
The "American block": 1 unit.
-
Total units to arrange around the table: 6+1=7 units.
2. Circular Arrangement
The number of ways to arrange n distinct objects around a circular table is given by the formula (n−1)!.
For our 7 units, the number of circular arrangements is:
3. Internal Arrangement
Within the "American block," the 3 Americans can be rearranged among themselves. Since they are distinct individuals, the number of ways to arrange them is:
4. Total Number of Ways
By the multiplication principle, we multiply the circular arrangement of the units by the internal arrangement of the group:
