Question

Arranging Books Five different mathematics books are to be arranged on a student's desk. How many arrangements are possible?

Short answer

There are 120 ways to arrange 5 books.

Step-by-step solution

Step 1. Given information.

The total number of books is 5.
We need to arrange books on a student's desk.

Step 2. Determine the possible ways of arrangement. 

This is an example of a permutation without repetition.

Permutation formula is:

$P(n,r)=\frac{n!}{(n-r)!}$

The number of ways to arrange 5 books is $\begin{array}{rcl}& & P(5,5)\end{array}$.

$\begin{array}{rcl}P(5,5)& =& \frac{5!}{(5-5)!}\\ & =& \frac{5!}{0!}\\ & =& \frac{5·4·3·2·1}{1}\\ & =& 120\end{array}$

Step 3. Conclusion.

There are 120 ways to arrange 5 books.