Question

"The organizer of a television show must select 5 people to participate in the show. The participants will be selected from a list of 21 people who have written in to the show. If the participants are selected randomly, what is the probability that the 5 youngest people will be selected?"

Answer 1

0.005% probability that the 5 youngest people will be selected.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, the order that the participants are chosen is not important. So the combinations formula is used.

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) = (n!)/(x!(n-x)!)`

If the participants are selected randomly, what is the probability that the 5 youngest people will be selected?"

Desired outcomes:

Five youngest.

The five youngest form a set of 5, and all 5 are chosen. So

`D = C_(5,5) = (5!)/(5!0!) = 1`

Total outcomes:

5 selected from a set of 21.

`T = C_(21,5) = (21!)/(5!16!) = 20349`

Probability:

`P = (D)/(T) = (1)/(20349) = 0.00005`

0.005% probability that the 5 youngest people will be selected.