# 1. Factorial Notation

For the following sections on counting, we need a simple way of writing the product of all the positive whole numbers up to a given number. We use factorial notation for this.

## Definition of n!

n factorial is defined as the product of all the integers from 1 to n (the order of multiplying does not matter) .

We write "n factorial" with an exclamation mark as follows: n!

n! = (n)(n − 1)(n − 2)...(3)(2)(1)

### Examples

a) 5! = 5 × 4 × 3 × 2 × 1 = 120

b) 10! = 10 × 9 × 8 ×... × 3 × 2 × 1 = 3,628,800

c) 0! = 1 (this is a convention)

d) 2! = 2

### Exercise

Find the value of: (10!)/(5!)

NOTE: We conclude from this answer and the answer for (d) above that we cannot simply cancel a fraction containing factorials. That is:

(10!)/(5!)!=2!

We use factorial notation throughout this chapter, starting in the Permutations section.

top

### Online Algebra Solver

This algebra solver can solve a wide range of math problems.

### Math Lessons on DVD

Easy to understand math lessons on DVD. See samples before you commit.

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.