Chapter 12.6, Problem 25PPE

To determine

To calculate: The number of ways books can be arranged.

Answer to Problem 25PPE

There are $5,040$ ways to arrange the books.

Explanation of Solution

Given information:

There are 10 books on the bookshelf. 4 of the books are read on summer 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.

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

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 number of books are - $10.$

Out of 10, 4 books are to be read on summer vacation.

  $\begin{array}{l}P{}_4=\frac{10!}{\left(10-4\right)!}\\ =\frac{10!}{6!}\\ =\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{6\times 5\times 4\times 3\times 2\times 1}\\ =10\times 9\times 8\times 7\\ =5,040\end{array}$

Hence, there are $5,040$ ways to arrange the books.