Subsets Of A Set Product

Question

I was asked the following question:

Let $A={1,2,3}$ and $B={4,5}$. How many subsets does the set $A\times B$ contain of size at most $4$?

My understanding of the outer product $A\times B$ is that it produces a set of ordered pairs containing every combination of the elements of $A$ and $B$. In this case, it would be a set of six ordered pairs, no subsets. Am I totally misunderstanding what is meant by $A\times B$ in this context?

Answer 1

Hint:

If a set has $n$ elements then it has exactly $\binom{n}{k}$ subsets of size $k$.