If there are $a$ ways of doing one thing and $b$ ways of doing another thing, then there are $ab$ ways of doing both things. This can be extended inductively.
Set theoretically, this is the definition of the product of cardinal numbers: \(\vert S_1\vert \cdot\vert S_2\vert \cdots\vert S_n\vert = \vert S_1\times S_2\times\cdots S_n\vert\) where $\vert \cdot\vert $ is the cardinal number of the sets $S_i$ and $\times$ is the Cartesian product of sets. The sets need not be finite nor does the number of sets.
Wikidata ID: Q557624