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Chapter 13: Q. 42 (page 855)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

Total number of professors is 8.

Professors required for the committee is 3.

02

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.

C(8,3)=8!(8-3)!3!=8!5!3!=8路7路6路5!5!路3路2路1=56

03

Step 3. Conclusion.

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

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