What is the total number of ways to choose both the committee and the President/Secretary?

To determine the total number of ways to choose both the committee and the President/Secretary, it is essential to first clarify the process of selection and the roles involved.

Assuming there is a certain number of members, let’s say 'n,' from which the committee needs to be formed. Typically, two roles need to be filled: a committee member and a distinct position such as President/Secretary.

First, a committee can be formed by selecting a group of members from the total pool. The number of combinations to choose a committee of size 'k' from a total of 'n' members is given by the binomial coefficient, which is represented as C(n, k) or "n choose k."

Once the committee is formed, the next task is to assign the roles of President and Secretary. If the committee consists of 'k' people, there are 'k' choices for President (since any committee member can be chosen), followed by 'k-1' choices for Secretary (the President cannot take on the role of Secretary).

Therefore, the total ways to select the committee and then assign the two roles is calculated as:

1. Choose the committee: C(n, k).

2. Assign the President: k choices.

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