Factorials
Product of integers up to n.
Key idea
Product of integers up to n.
In depth
n! = n(n − 1)...1 counts the ways to arrange n distinct objects, with 0! = 1 by convention. Factorials grow faster than exponentials.
Worked example
5! = 120 arrangements of 5 books. 7!/5! = 7 × 6 = 42.
Formula
Real-world uses
- Counting arrangements of a sports team or the orderings of tasks in a schedule
Common mistake
Setting 0! = 0.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Factorials?
Product of integers up to n. It is a topic at the intermediate level in Discrete Math & Number Theory.
What is the formula for Factorials?
The key formula is n! = n(n−1)…1.
Where is Factorials used in real life?
Real-world examples: Counting arrangements of a sports team or the orderings of tasks in a schedule.
What should I learn before Factorials?
Make sure you are comfortable with Rule of Sum and Product, the previous topic in Discrete Math & Number Theory.
What is a common mistake with Factorials?
Setting 0! = 0.
How can I practise Factorials?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Factorials?
Move on to Permutations with Repetition next.
Related intermediate topics in Discrete Math & Number Theory
- Statements and Truth Values – A proposition is true or false, never both.
- Logical Connectives – AND, OR, NOT, implication and biconditional.
- Truth Tables – List all truth assignments to evaluate compound statements.
- Subsets and Power Sets – A set with n elements has 2ⁿ subsets.
- Set Operations – Union, intersection, difference and complement.
- Venn Diagrams – Pictures of sets and their overlaps.