Questions: You have 13 different video games. How many different ways can you arrange the games side by side on a shelf? You can arrange the 13 different video games in different ways.

You have 13 different video games. How many different ways can you arrange the games side by side on a shelf?

You can arrange the 13 different video games in different ways.

Transcript text: You have 13 different video games. How many different ways can you arrange the games side by side on a shelf? You can arrange the 13 different video games in $\square$ different ways.

Solution

Solution Steps

Step 1: Understand the Problem

We are given $n$ different items and asked to find the number of different ways to arrange them side by side on a shelf. This is a permutations problem where the order of arrangement matters.

Step 2: Identify the Formula

The formula to find the number of arrangements (permutations) of $n$ items is $n!$, which stands for the factorial of $n$. The factorial of a number $n$ is the product of all positive integers less than or equal to $n$.

Step 3: Apply the Formula

For $n = 13$, the calculation is $n! = 13! = 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 6227020800$.