# Factorial Calculator

Examples:

## What is a factorial?

The factorial function is a mathematical formula denoted by the exclamation mark "!" or n!

### Purpose

Factorials are often used in the calculation of permutations and combinations, as well as in the coefficients of terms of binomial expansions.

If the order of things matters, permutations tell us how many different ways we can organize them. Combinations inform us how many different ways we can select k from n things if their order is irrelevant.

### What does factorial represent?

It represents a non-negative integer obtained by multiplying all the positive integers less than or equal to n. n! (also known as n factorial) is defined for all positive integers as

n! =n(n−1) (n−2) ⋯ (1)

In other words, n! represents the sum of all positive integers that are less than or equal to n.

## Examples of Factorial

### Factorial of 6

6! = 6 × 5 × 4 × 3 × 2 ×1

6! = 720

Therefore, the factorial of 6 is 720.

### Factorial of 10

10! = 10× 9 × 8 × 7 × 6 × 5× 4 × 3 × 2 × 1

10! = 3,628,800

Therefore, the factorial of 10 is 3,628,800.

### Factorial of 0

The factorial of 0 is one, which means that 0! = 1.

According to the convention of empty product, the consequence of multiplying no factors is a nullary product. This implies that the convention is the multiplicative identity.

## Factorial Problems

### What if we just had to organize two of the six books on the shelf?

We have six different books, n = 6. We only arrange two of the books, so k = 2. Let us enter the following values into our formula:

n! / (n-k)!

6! / (6 - 2)! = 6! / 4!

If we add up all of the variables in each factorial, we get the following:

(6 ×5 × 4 × 3 × 2 × 1) / (4 × 3 × 2 × 1)

We can cancel 4 × 3 × 2 × 1 from the numerator and denominator to get 6 × 5, which equals 30.