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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.

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

03

Step 3. Conclusion.

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

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Most popular questions from this chapter

Find the probability of the indicated event if $P (A) = 0.25 a n d P (B) = 0.45$

$P (A \cap B) i f P (A \cup B) = 0.6$

Find the probability of the indicated event if $P (A) = 0.25 a n d P (B) = 0.45$

$P (A \cap B)$ if A and B are mutually exclusive.

A(n) _____________ is an ordered arrangement of $r$ objects chosen from $n$ objects.

In a probability model, which of the following numbers could be the probability of an outcome?

$1.5, \frac{1}{2}, \frac{3}{4}, \frac{2}{3}, 0, - \frac{1}{4}$

Find the value of each permutation.

$P (4, 4)$

See all solutions

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