Chapter 13.2, Problem 50AYU

Forming a Committee The student relations committee of a college consists of 2 administrators, 3 faculty members, and 5 students. Four administrators, 8 faculty members, and 20 students are eligible to serve. How many different committees are possible?

To determine

To find: How many different committees are possible?

Answer to Problem 50AYU

5209344

Explanation of Solution

Given:

The student relations committee of a college consists of 2 administrators, 3 faculty members, and 5 students. Four administrators, 8 faculty members, and 20 students are eligible to serve.

Formula used:

$C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

The committee of 2 administrators, 3 faculty members, and 5 students to be chosen from 4 administrators, 8 faculty members, and 20 students.

Number of choices for administrators is $C\left(4,2\right)=\frac{4!}{2!*2!}=6$.

Number of choices for 3 faculty members is $C\left(8,3\right)=\frac{8!}{5!3!}=56$.

Number of choices for 5 students is $C\left(20,5\right)=\frac{20!}{5!15!}=15504$.

Hence, number of choices for forming a committee of 2 administrators, 3 faculty members, and 5 students are $6*56*15504=5209344$.