If there are 5 members in the committee, how many ways can a President and a Secretary be chosen?

To determine how many ways a President and a Secretary can be chosen from a committee of 5 members, it's important to recognize that these are two distinct positions.

First, you can select the President from any of the 5 members. After a President has been chosen, there are 4 remaining members available to fill the position of Secretary. Therefore, the total number of ways to choose a President and a Secretary can be calculated by multiplying the number of choices for each position:

1. Choose 1 from 5 for the President: 5 choices.

2. Choose 1 from the remaining 4 for the Secretary: 4 choices.

Thus, the total number of combinations is 5 (for President) multiplied by 4 (for Secretary), which results in 20 different ways to choose the two officers.

This calculation reinforces the concept of permutations when order matters since the roles of President and Secretary are distinct, leading to the final answer of 20.