Solve the problem. the organizer of a television show must select 5 people to participate in the show. the participants will be selected from a list of 30 people who have written in to the show. if the participants are selected randomly and none of the 30 people are the same age, what is the probability that the 5 youngest people will be selected?

Step-by-step explanation:

Combination question

Generally

nCr = n! / (n-r)!r!

The organizer want to select 5 people from 30 people

Then, the total possible selection is

30C5 = 30! / (30-5)!5!

30C5 = 30•29•28•27•26•25!/25! ×5!

30C5 = 17,100,720 /5•4•3•2

30C5 = 142,506 ways

So, there are 142,506 numbers of ways to selected them.

The group of 5 youngest persons of 30 is UNIQUE such group of 5 persons from 30, under given conditions..

if there are exactly 5 youngest people and if they were all selected, the probability is

5 / 142,506 = 0.000035086