Question

we want to build upua committee with 5 people on campus but jack was already selected for the president position. in how many ways can we select the committee from a pool of 10 people?

Answer 1

There are 126 different ways to select the remaining 4 committee members from a pool of 9 people, after accounting for the president's position already being filled.

Step-by-step explanation:

In this mathematics problem, we're interested in determining the number of ways to select a committee of 5 people from a pool of 10, given that the president's position has already been filled by Jack. Since Jack's position reduces the pool of available candidates to 9, and we need to select 4 more committee members (totaling 5 with the president), we are looking for the number of combinations of 4 people from the remaining 9.

The formula for combinations (often denoted as C(n, k) or n choose k) where n is the total number of items to choose from, and k is the number of items to choose, is given by:

C(n, k) = n! / (k! * (n - k)!)

Plugging in our numbers, we get C(9, 4) which is equal to:

9! / (4! * (5!)) which simplifies to (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) which equals 126.

Therefore, there are 126 different ways to select the committee members.