# Factorial Formula

Factorial formula is used to find the factorial of a number. A factorial is defined as the product of the number with all its lowest value numbers. It is also defined as multiplying the descending series of numbers. The symbol used to denote factorial is !. It should be noted that the factorial of 0 is 1. The factorial formula is mostly used in permutations and combinations for probability calculation.

## Formula for Factorial n

The Factorial Formula is given as,

 n Factorial Formula n! = 1 × 2 × 3 × ….. × (n − 1) × n

Check: Factorial Calculator

### Solved Examples Using Factorial Formula

Question 1: What is 8!?

Solution:

The formula formula for factorial is,

n! = 1 × 2 × 3 × ………. × (n-1) × n

8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8

8! = 40320

Question 2: What is $\frac{9!}{5!}$?

Solution:

The formula formula for factorial is,

n! = 1 × 2 × 3 × ………. × (n-1) × n

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

5! = 1 × 2 × 3 × 4 × 5

$\frac{9!}{5!} = \frac{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 }{1 \times 2 \times 3 \times 4 \times 5}$

On simplification we get,

$\frac{9!}{5!}$ = 6 × 7 × 8 × 9

$\frac{9!}{5!}$ =3024