Chapter 13.2, Problem 42AYU

Establishing Committees In how many ways can a committee of 3 professors be formed from a department that has 8 professors?

To determine

To find: In how many ways can a committee of 3 professors be formed from a department that has 8 professors?

Answer to Problem 42AYU

56 ways a committee of 3 professors be formed from a department that has 8 professors.

Explanation of Solution

Given:

Committee of 3 professors be formed from a department that has 8 professors.

Formula used:

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

Calculation:

Selection of committee of 3 professors be formed from a department that has 8 professors can be represented by $C\left(8,3\right)$.

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

$C\left(8,3\right)=\frac{8!}{\left(8-3\right)!3!}$

$C\left(8,3\right)=\frac{8*7*6*5!}{3!5!}$

$C\left(8,3\right)=56$