ms. bells mathematics class consists of 7 sophomores, 13 juniors, and 12 seniors. how many different ways…

ms. bells mathematics class consists of 7 sophomores, 13 juniors, and 12 seniors. how many different ways can ms. bell create a 5 - member committee of seniors if each senior has an equal chance of being selected?

ms. bells mathematics class consists of 7 sophomores, 13 juniors, and 12 seniors. how many different ways can ms. bell create a 5 - member committee of seniors if each senior has an equal chance of being selected?

Answer

Explanation:

Step1: Identify combination formula

We use the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be chosen. Here, $n = 12$ (total number of seniors) and $r=5$ (number of seniors to be on the committee).

Step2: Calculate factorial values

$n!=12! = 12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1$, $r!=5!=5\times4\times3\times2\times1$, and $(n - r)!=(12 - 5)!=7!=7\times6\times5\times4\times3\times2\times1$. Then $C(12,5)=\frac{12!}{5!(12 - 5)!}=\frac{12!}{5!7!}=\frac{12\times11\times10\times9\times8\times7!}{5\times4\times3\times2\times1\times7!}$.

Step3: Simplify the expression

Cancel out the $7!$ terms. We have $\frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1}=\frac{95040}{120}=792$.

Answer:

792