How many different 10 person committees can be selected from a pool of 23 people?
(this is using permutations and combinations)

We're going to be using combination since this question is asking how many different combinations of 10 people can be selected from a set of 23.

We would only use permutation if the order of the people in the committee mattered, which it seems it doesn't.

Formula for combination:

Where represents the number of objects/people in the set and represents the number of objects/people being chosen from the set

There are 23 people in the set and 10 people being chosen from the set

Usually I would prefer solving such fractions by hand instead of a calculator, but factorials can result in large numbers and there is too much multiplication. Using a calculator, we get

Thus, there are 1,144,066 different 10 person committees that can be selected from a pool of 23 people. Let me know if you need any clarifications, thanks!

~ Padoru

21

step-by-step explanation: