Chapter 12.6, Problem 54PPE

To determine

To show: whether the situation is a permutation problem or a combination problem. Also, to calculate the number of different orders person could read the 4 books.

Answer to Problem 54PPE

The situation is of permutation problem. There are $24$ different orders possible to read the books.

Explanation of Solution

Given information:

You take 4 books out of the school library to read during spring vacation.

Formula used:

A permutation is an arrangement of objects in a specific order. The expression $P{}_r$ represents the number of permutations of $n$ objects arranged $r$ at a time.

  $P{}_r=\frac{n!}{\left(n-r\right)!}$

A combination is a selection of objects without regard to order. The expression $C{}_r$ represents the number of combination of $n$ objects chosen $r$ at a time.

  $C{}_r=\frac{n!}{r!\left(n-r\right)!}$

For any positive integer $n$, the expression $n$ factorial is written as $n!$ and is the product of integers from n down to 1.

Calculation:

According to the question ,

The person has to read the books in order. Therefore, the situation is a permutation problem.

Number of books are 4.

Number of books to be read in order are 4.

  $\begin{array}{l}P{}_4=\frac{4!}{\left(4-4\right)!}\\ =\frac{4!}{0!}\\ =\frac{4\times 3\times 2\times 1}{1}\\ =4\times 3\times 2\times 1\\ =24\end{array}$

Hence, there are $24$ different orders of books person could read.