Multiplication Principle

Topics: Combinatorics - Probability

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The multiplication principle is a basic counting principle.

Intuitively, it tells us that if we have two sets of $k$ and $n$ elements respectively, and we want to choose two elements such that one is from the first set and the other from the second one, then we can do so in $kn$ ways.

And

Notice that “and” is the keyword for multiplication. It tells us that we take into consideration both sets, not one or the other.

Compare this with addition, which uses “or”.

Mathematically, if $A$ and $B$ are two finite sets, then:

$$|A\times B|=|A||B|$$

Example

Let’s say we’re shopping for a laptop.

We can choose from $4$ different processor options, $3$ storage options and $2$ size options.

In total, we can choose from $4(3)2=24$ options.