A company manager wants to form a committee. There are 12 staff members. He wants to choose the members of the committee from these 12 people. Two specific people, A and B, must both be on the committee. How many ways can the committee be formed? Note that the problem does not specify the size of the committee. We are given that at least two members are required for the committee.

1. Problem Description

A company manager wants to form a committee. There are 12 staff members. He wants to choose the members of the committee from these 12 people. Two specific people, A and B, must both be on the committee. How many ways can the committee be formed? Note that the problem does not specify the size of the committee. We are given that at least two members are required for the committee.

2. Solution Steps

Since A and B must be on the committee, we need to choose the remaining members from the other $12 - 2 = 10$ staff members.

The remaining members can be any number of people from 0 to

1

0. This means that any subset of the 10 remaining staff members can be included in the committee.

The number of such subsets is $2^{10}$, since each of the 10 staff members can either be included in the committee or not. The total number of possible committees is equal to the number of subsets of the set of 10 remaining staff members, which is $2^{10}$.

$2^{10} = 1024$.

3. Final Answer

1024