Question

from a group of 12 people, you randomly select 5 of them. what is the probability that they are the 5 oldest people in the group? give your answer as a fraction

Explanation:

Step1: Calculate total combinations

The number of ways to choose 5 people out of 12 is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 12$ and $r=5$. So $C(12,5)=\frac{12!}{5!(12 - 5)!}=\frac{12!}{5!7!}=\frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1}=792$.

Step2: Determine favorable combinations

There is only 1 way to select the 5 - oldest people.

Step3: Calculate probability

Probability $P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}=\frac{1}{792}$.

Answer:

$\frac{1}{792}$