Number of Set Products
Result
Suppose $A$ and $B$ are finite sets.
Then $\num{A \times B} = \num{A} \times
\num{B}$.
The proof involves induction on the size of
one of the sets, and will, I believe, use the
result of the number of a disjoint union; thus
the dependence on the sheet Number of Disjoint Unions.
This is often called the multiplication principle, rule of product, or the fundamental principle of counting.