Question

How many different 10 person committees can be selected from a pool of 23 people?

Answer 1

Answer:

1st combinations 2nd permutations

Step-by-step explanation:

Answers on edgenuity :)

Answer 2

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:

$C(n,r)=\dfrac{n!}{(n-r)!r!}$

Where $n$ represents the number of objects/people in the set and $r$ 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

$C(23,10)=\dfrac{23!}{(23-10)!10!}$

$=\dfrac{23!}{13!\times10!}$

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

$=1,144,066$

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