To determine how many ways 5 different books can be stacked on a shelf, we use the concept of permutations, because the order in which the books are arranged matters.
1. Identify the total number of books: There are 5 different books.
2. Utilize the factorial formula: The number of ways to arrange [tex]\( n \)[/tex] different items is calculated by [tex]\( n! \)[/tex] (n factorial). Factorial of a number [tex]\( n \)[/tex] is the product of all positive integers from 1 to [tex]\( n \)[/tex].
For example:
[tex]\[
5! = 5 \times 4 \times 3 \times 2 \times 1
\][/tex]
3. Perform the calculation (conceptually):
- [tex]\( 5! = 5 \times 4 \times 3 \times 2 \times 1 \)[/tex]
- Multiplying these numbers together:
- [tex]\( 5 \times 4 = 20 \)[/tex]
- [tex]\( 20 \times 3 = 60 \)[/tex]
- [tex]\( 60 \times 2 = 120 \)[/tex]
- [tex]\( 120 \times 1 = 120 \)[/tex]
4. Conclusion: The total number of ways to stack 5 different books on a shelf is 120.
So, the correct answer is:
120
