A round table conference is attented by 3 Indians,
3 Chinese, 3 Canadians and 2 Americans. Find
the no of ways of arranging them at the round
table so that the delegates belonging the same
country sit together

Given Indians -3
Chinese -3
Canadians - 3
Americans - 2
consider 3 Indians are 1 unit + 3chainese are 1
unit + 3 Canadians are 1 unit + 2
Americans are 1 unit = 4 units
The 4 units are arranged in round table
=(4 - 1)! = 3!
The 3 Indians are arranged Among themselves
= 3!
The 3 Chinese are arranged Among themselves
= 3!
The 2 Americans are arranged Among themselves
= 2!
required arrangement = $3!\times 3!\times 3!\times 3!\times 2!=2592$