Factorial is a mathematical concept represented by an exclamation point (!). The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. For example, the factorial of 5 is 5! = 5 x 4 x 3 x 2 x 1 = 120. The factorial function can be defined as: n! = n * (n-1) * (n-2) * ... * 2 * 1, where n! = 1 if n = 0 or n = 1.
The basic formula for the factorial of a positive integer n is:
n! = n * (n-1) * (n-2) * ... * 2 * 1
where n! = 1 if n = 0 or n = 1.
Here are some rules for working with factorials:
The factorial of 0 (0!) is defined to be 1.
The factorial of a positive integer n (n!) is equal to n times the factorial of n-1.
Factorials grow rapidly and can become very large very quickly. For example, 20! (the factorial of 20) is 2432902008176640000.
Factorials have several useful properties, such as the relationship between n! and (n-1)! (n! = n * (n-1)!).
Factorials are commonly used in counting problems, probability and statistical calculations, and mathematical modeling.
The factorial of a positive integer n can be calculated by multiplying all positive integers less than or equal to n. For example, the factorial of 5 (5!) can be calculated as follows:
5! = 5 * 4 * 3 * 2 * 1 = 120