The fundamental principle of counting

Before any formula there is a single idea from which everything follows: when an action is made up of successive choices, the counts multiply.

Property — The multiplication principle

If an action can be carried out in $m$ ways, and, for each of them, a second action can be carried out in $n$ ways, then the pair of actions can be carried out in $m\cdot n$ ways.

This is the building block of all the later formulae. For example, if I want to choose a shirt (5 available) and a pair of trousers (3 available) for an outfit, I have $5\cdot 3 = 15$ possible outfits.

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Topics: Combinatorics
Concepts: Combinatorial calculus · Multiplication principle
Methods: Counting principle
Skills: Combinatorial calculus