# Factorial Formula

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 !. The factorial of 0 is 1. Factorial Formula is mostly used in permutations and combinations for probability calculation.

The Factorial Formula is given as,

$\LARGE n! \; = 1 \; \times 2 \; \times 3 \; \times ….. \; \times \; (n-1) \; \times n$

### Solved Examples

Question 1: What is 8! ?

Solution:

The formula formula for factorial is,

n! = $1 \times 2 \times 3 \times ………. \times (n-1) \times n$

8! = $1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8$

8! = 40320

Question 2: What is $\frac{9!}{5!}$?

Solution:

The formula formula for factorial is,

n! = $1 \times 2 \times 3 \times ………. \times (n-1) \times n$

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

5! = $1 \times 2 \times 3 \times 4 \times 5$

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

$\frac{9!}{5!}$ = $6 \times 7 \times 8 \times 9$

$\frac{9!}{5!}$ = 3024