Question

you need to arrange five of your favorite books along a small shelf. how many different ways can you arrange the books, assuming that the order of the books makes a difference in you?
ways
(type a whole number )

Explanation:

Step1: Identify the problem type

This is a permutation problem where we need to arrange \( n = 5 \) distinct items (books) in order. The formula for permutations of \( n \) distinct objects is \( P(n,n)=\frac{n!}{(n - n)!}=n! \).

Step2: Calculate the factorial

The factorial of a number \( n \) is defined as \( n!=n\times(n - 1)\times(n - 2)\times\cdots\times1 \). For \( n = 5 \), we have \( 5!=5\times4\times3\times2\times1 \).

Calculating step - by - step:
\( 5\times4 = 20 \)
\( 20\times3=60 \)
\( 60\times2 = 120 \)
\( 120\times1=120 \)

Answer:

\( 120 \)