Factorial Notation Study Guide

Definition

Factorial notation is the product of all positive integers from 1 to a given number.

Notation

The factorial of a number n is denoted by the symbol "n!"

Example

If we have 5!, it means 5 × 4 × 3 × 2 × 1 = 120.

Calculation

To calculate the factorial of a number, simply multiply all the positive integers from 1 up to that number.

Properties

• 0! = 1
• 1! = 1
• n! = n × (n-1)!

Applications

Factorial notation is commonly used in combinatorics, probability, and to solve problems involving permutations and combinations.

Practice Problems

1. Calculate the value of 4!
2. Find the value of 6! - 5!

1. Calculate the value of 4!
   4! = 4 × 3 × 2 × 1 = 24
2. Find the value of 6! - 5!
   6! - 5! = (6 × 5 × 4 × 3 × 2 × 1) - (5 × 4 × 3 × 2 × 1) = 720 - 120 = 600