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Fundamental Counting Principles

Class: AA HL, AA SL, AI SL, AI HL

The Fundamental Counting Principle states that if there are n ways to do one thing and m ways to do another thing, then there exist n x m ways to do both things.

Note: The Fundamental Counting Principle is also called the Counting Rule.

Definitions

Fundamental Counting Principle: When choosing an option for n and an option for m, then there exist n x m different possibilities.
Independent events: If the occurrence of one event does not interfere with the occurrence of the other event.
Dependent events: Two events are dependent if the occurrence of one event affects the likelihood of the occurrence of the other event.

More than two choices

Consider a situation in which there exist n options to do something one way, m options to do something the other way, and g options to do it a third way. Thus we have n x m x g possible combinations. As you can see the Counting Rule applies to a finite number of options.

Basic Formula

Event 1: a₁ ways
Event 2: a₂ ways
Event 3: a₃ ways
.
.
.
Event n: a_n ways

Thus, there exist a₁ x a₂ x a₃ x … x a_n total combinations.

Independent vs Dependent

If the events are dependent events, then the Fundamental Counting Principle does not apply as there exist different outcomes based on different events.

Video Explanation

Practice

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