Chapter 11, Problem 26CCSR

Solution

a)

To explain: Whether the provided situation is a problem of combination or permutation.

It is a problem of combination rule.

Given information:

4 out of 30 employees are being selected as employees of the month by an employer.

Concept used:

There are two types of rules that are applied to do the selection of items. These are:

1. Combination rule: It is a rule that is applied when the order is not a matter of concern for the selection of items.
2. Combination rule: It is a rule that is applied when the order is a matter of concern for the selection of items.

Explanation:

In this case, it is given that 4 out of 30 employees are being selected as employees of the month by an employer. Here, order of the employees in not of concern.

Hence, the provided problem is a situation of combination.

b)

To find: The different possible selections.

The number of selections is 220.

Calculation:

The number of selections could be calculated as:

  $\begin{array}{c}C\left(n=12,r=3\right)=\frac{12!}{3!\left(12-3\right)!}\\ =\frac{12!\times 11!\times 10!\times 9!}{3\times 2\times 1\times 9!}\\ =220\end{array}$

The required number of selections is 220.