Question

Establishing Committees In how many ways can a committee of 4 students be formed from a pool of 7 students?

Short answer

The number of different committees that can be formed is 35.

Step-by-step solution

Step 1. Given information.

Total number of students is 7.

Students required for the committee is 4.

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 7 objects taken 4 at a time.

$\begin{array}{rcl}C(7,4)& =& \frac{7!}{(7-4)!4!}\\ & =& \frac{7!}{3!4!}\\ & =& \frac{7·6·5·4!}{3·2·1·4!}\\ & =& 35\end{array}$

Step 3. Conclusion.

The number of different committees that can be formed is 35.