The multiplication principle is a basic counting principle.
Intuitively, it tells us that if we have two sets of and 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 ways.
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 and are two finite sets, then:
Let’s say we’re shopping for a laptop.
We can choose from different processor options, storage options and size options.
In total, we can choose from options.