Chapter 12.6, Problem 53PPE

To determine

To show: whether the situation is a permutation problem or a combination problem. Also, to calculate the number of books one can select.

Answer to Problem 53PPE

The situation is of combination problem. There are $56$ different sets possible to select 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 select the books. Therefore, the situations is a combination problem.

Number of books are 8.

Number of books to be selected are 3.

  $\begin{array}{l}C{}_3=\frac{8!}{3!\left(8-3\right)!}\\ =\frac{8!}{3!5!}\\ =\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1\times 3\times 2\times 1}\\ =\frac{8\times 7\times 6}{3\times 2\times 1}\\ =8\times 7\\ =56\end{array}$

Hence, there are $56$ different sets of books person could select.