Final answer:
There are 5,040 different ways to arrange 7 books on a shelf, calculated by 7 factorial (7!).
Step-by-step explanation:
The question asks about the different ways you can arrange 7 books on a shelf. To answer it, you need to understand the concept of permutations. In the context of arranging books on a shelf, where the order matters, the number of ways to arrange 'n' unique items is given by n! (n factorial), which is the product of all positive integers from 1 to 'n'. So, for 7 books, the calculation would be 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1, which equals to 5,040 ways. Each arrangement is unique because the position of each book matters in this scenario.