Why are pushdown automata countable?
Since you don't provide any attempt on your own part, note two things.


The definition of countability.


  A set $A$ is countable if and only if $A$ is finite or there is a bijection $f : A \to \mathbb{N}$.

How do you represent pushdown automata in a formal way?


If you digest the first item and answer the second, the answer should become apparent.