Question

From a group of 40 people, a jury of 12 people is to be selected. In how many different ways can the jury be selected?

Answer 1

Answer:

The jury can be selected in 5,586,853,480 different ways.

Step-by-step explanation:

The order is not important.

Suppose the jury had two members.

John and Laura would be the same jury as Laura and John.

So we use the combinations formula to solve this problem.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

From a group of 40 people, a jury of 12 people is to be selected. In how many different ways can the jury be selected?

This is combinations of 12 people from a set of 40 people. So

$C_{40,12} = \frac{40!}{12!(28)!} = 5,586,853,480$

The jury can be selected in 5,586,853,480 different ways.