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)
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
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:
We use factorial notation throughout this chapter, starting in the Permutations section.
Didn't find what you are looking for on this page? Try search:
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Go to: Online algebra solver
Ready for a break?
Play a math game.
(Well, not really a math game, but each game was made using math...)
The IntMath Newsletter
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!
Short URL for this Page
Save typing! You can use this URL to reach this page:
Math Lessons on DVD
Easy to understand math lessons on DVD. See samples before you commit.
More info: Math videos