📚 About Factorials

Definition: The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

Formula:

• n! = n × (n-1) × (n-2) × ... × 2 × 1
• 0! = 1 (by definition)
• 1! = 1

Common Factorial Values:

n	n!	Calculation
0	1	0! = 1 (by definition)
1	1	1! = 1
2	2	2! = 2 × 1
3	6	3! = 3 × 2 × 1
4	24	4! = 4 × 3 × 2 × 1
5	120	5! = 5 × 4 × 3 × 2 × 1
6	720	6! = 6 × 5 × 4 × 3 × 2 × 1
7	5,040	7! = 7 × 6!
8	40,320	8! = 8 × 7!
9	362,880	9! = 9 × 8!
10	3,628,800	10! = 10 × 9!

Applications:

• Combinatorics: Counting permutations and combinations
• Probability: Calculating probabilities in statistics
• Mathematics: Series expansions and mathematical analysis
• Computer Science: Algorithm analysis and recursive functions

Properties:

• Factorials grow very rapidly (factorial growth)
• n! = n × (n-1)! (recursive definition)
• Factorials are only defined for non-negative integers
• Large factorials require special handling due to size