Factorial Notation Study Guide

What is Factorial Notation?

Factorial notation is a mathematical notation used to represent the product of all positive integers up to a given number. It is denoted by the exclamation mark (!) placed after a number.

Example

The factorial of a positive integer n, denoted as n!, is the product of all positive integers from 1 to n.

For example, 5! (read as "5 factorial") is calculated as: 5! = 5 x 4 x 3 x 2 x 1 = 120.

Properties of Factorial Notation

1. n! = n x (n-1) x (n-2) x ... x 2 x 1
2. 0! = 1 (by definition)
3. 1! = 1 (by definition)

Calculating Factorials

To calculate the factorial of a number, start with the given number and multiply it by all positive integers less than itself, down to 1.

For example, to calculate 6!, you would perform the following multiplication: 6 x 5 x 4 x 3 x 2 x 1 = 720.

Applications

Factorial notation has applications in combinatorics, permutations, and probability, where it is used to count the number of ways to arrange or select items.

Study Tips

• Practice calculating factorials of different numbers to become familiar with the notation.
• Understand the properties of factorial notation and how it is used in different mathematical contexts.
• Explore real-world applications of factorial notation to gain a deeper understanding of its significance.