Counting Principles
Counting principles help us determine how many ways events can occur. The multiplication principle, tree diagrams, and lists are key tools for systematic counting.
What You Need to Know
Key Concept Diagram
Multiplication principle: if one event has m outcomes and another has n, together they have m x n outcomes
A tree diagram shows all possible outcomes in a branching structure
Listing all outcomes systematically helps calculate probability
Factorial notation: n! = n x (n-1) x ... x 2 x 1, used to count arrangements
Key Vocabulary
Outcome
A possible result of an event or experiment
Sample space
The set of all possible outcomes of an experiment
Tree diagram
A branching diagram showing all possible outcomes of a sequence of events
Factorial
The product of all positive integers up to n, written n!; e.g. 3! = 6
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A lunch menu has 3 mains and 4 desserts. How many different meal combinations are possible?
Question 2
How many 2-letter arrangements can be made from the letters A, B, C if no letter is repeated?
Question 3
What does 4! equal?
Key Concepts Summary
- ●Multiplication principle: if one event has m outcomes and another has n, together they have m x n outcomes
- ●A tree diagram shows all possible outcomes in a branching structure
- ●Listing all outcomes systematically helps calculate probability
- ●Factorial notation: n! = n x (n-1) x ... x 2 x 1, used to count arrangements