Question

A class with 24 students is forming a committee of 4 persons with a chair and three general members. How many different committees could be chosen?

Answer 1

To determine the number of different committees that can be formed from a class of 24 students with a chair and three general members, you first select the chairperson (24 ways), then choose the three general members from the remaining students (23C3 combinations). The total number of different committees is 24 x 1771 = 42,504.

Step-by-step explanation:

The question asks about the number of different committees that could be formed from a class of 24 students with 1 chair and 3 general members. To solve this, we first select a chairperson, and then we choose the remaining three general members.

1. We have 24 choices for the chairperson.
2. For the remaining three members, we no longer consider the chairperson, leaving us with 23 students to choose from. This is a combination problem where we are choosing 3 students out of the remaining 23 without regard to order.
3. The number of ways to choose 3 students out of 23 is calculated using the combination formula: 23C3, which is 1771.
4. Multiplying the number of ways to choose a chairperson (24) by the number of ways to choose the other three members (1771) gives us the total number of different committees: 24 x 1771 = 42,504.