Question

Find the number of ways of forming a committee of 5 members out of 7 Indians and 5 Americans, so that always Indians will be the majority’ in the committee.

Answer 1

We need a majority of Indian’s which is obtained as follows.

Indians	Americans
7	5
5	0
4	1
3	2

The possible ways are (5I) or (4I and 1A) or (3I and 2A)