I'm trying to show whether the following sets are countable:

$\mathcal{P}\_2(\mathbb{N})~~,~~\mathcal{P}\_2(\mathbb{R})$ 

where $\mathcal{P}\_2 (X)$ is the set of all subsets of $X$ containing exactly two elements.

For the first one, I'm thinking that, if I can find a surjective map $f: \mathbb{N} \to \mathcal{P}\_2 (\mathbb{N})$ I'm done, but I can't come up with one.

The second one I'm not too sure about. I know that it is uncountable, but I don't really know where to start.

My analysis skills are pretty rusty to say the least, so any help on how one would generally go about solving this would be much appreciated! :-)