Question

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

Short answer

The number of different committees that can be formed is 56.

Step-by-step solution

Step 1. Given information.

Total number of professors is 8.

Professors required for the committee is 3.

Step 2. Determine the number of committees.

The order of being selected for a committee is not significant. So, the problem asks for the number of combinations of 8 objects taken 3 at a time.

$\begin{array}{rcl}C(8,3)& =& \frac{8!}{(8-3)!3!}\\ & =& \frac{8!}{5!3!}\\ & =& \frac{8·7·6·5!}{5!·3·2·1}\\ & =& 56\end{array}$

Step 3. Conclusion.

The number of different committees that can be formed is 56.