The factorial of a number, denoted by that number followed by an exclamation mark (e.g., 9!), is the product of all positive integers up to that number. In simpler terms, it’s a way to find out how many different ways you can arrange a set of items.
For the number 9, the factorial can be calculated as follows:
9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
If we break that down step by step:
- 9 × 8 = 72
- 72 × 7 = 504
- 504 × 6 = 3024
- 3024 × 5 = 15120
- 15120 × 4 = 60480
- 60480 × 3 = 181440
- 181440 × 2 = 362880
- 362880 × 1 = 362880
Thus, the factorial of 9 is 362880. This means there are 362880 possible arrangements of a set of 9 distinct items. Factorials are used in various fields, including mathematics, statistics, and computer science, particularly in permutations and combinations.