Product Rule (Combinatorics)

combinatorics

Definition

Product Rule ( Combinatorics)

If there are $n$ ways to perform action 1 followed by $m$ ways to perform action $2$, then there are $n\times m$ ways to perform action $1$ followed by action $2$.

Let $S_1$ and $S_2$ be two finite sets, then:

$$|S_1\times S_2|=|S_1|\cdot |S_2|$$