Question

How many different 3 people committees can be formed from a group of 25 people?

Answer 1

Use the combination formula, `(n!) / {r!(n - r)!`

Explanation:

This problem is a combination problem since order doesn't matter.

n = the total number of elements, in this case 25

r = the number being picked, in this case 3

Plug n and r into the formula:

`(25!) / {3!(25 - 3)!`

= `(25!) / {3!(22)!`

= 2300

So, there are 2300 different committees that can be formed.

Here is a problem for you practice:

1. Solve the following problem.

14 people apply for a job. Only 2 positions are available. Find the number of different combinations of employees possible.