Question

There are 8 members in a club of which A and B are the two members. A committee of 5 is to be formed, How many of these will include A and exclude B?

Answer 1

Solution:-

There are total 8 members in the club out of which A and B are members. The other 6 persons are unknown.
It is required to form a committee in which A is a member but B is not a member.
So, a committee of 5 persons will always contain the 1 member A.
The other four members must be chosen from the 6 unknown persons since B cannot be included as a member in the committee.
The number of ways in which 4 persons can be chosen from 6 unknown persons are = 6c₄ 
= (6*5*4*3)/(4*3*2*1)
= 15 ways
Answer.