Question

1. 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, what is the probability that the 5 youngest people will be selected? a) $\frac{1}{142,506}$ b) $\frac{1}{17,100,720}$ c) $\frac{4}{15}$ d) $\frac{1}{120}$

Explanation:

Step1: Calculate total number of combinations

The number of ways to choose 5 people out of 30 is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 30$ and $r=5$. So $C(30,5)=\frac{30!}{5!(30 - 5)!}=\frac{30!}{5!×25!}=\frac{30\times29\times28\times27\times26}{5\times4\times3\times2\times1}=142506$.

Step2: Calculate the number of favorable combinations

There is only 1 way to select the 5 youngest people.

Step3: Calculate the probability

The probability $P$ of an event is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{1}{142506}$.

Answer:

A. $\frac{1}{142,506}$