Hello! (Hi)

So I am just starting out with combinations and I'm a little confused and could very much use some advice. I'm working on a problem, and I keep running in circles, so let me start from there.

The problem is:

"How many hands in a 5-card poker hand can have exactly 1 pair (2 of the same kind) in a 52 card deck?"

This is what I've tried to do:

Order doesn't matter, so I figure it'scombinations.

To have a pair, I need one card from a suit of 13 cards, and another card from a different suit of 13 cards. There are 4 suits in a deck.

So I took one card from the first suit C(13,1) and then add it to one card from another suit C(13,1) and add them to the other 3 cards in a hand, C(52,3)?

And the final answer would be...

C(13,1) + C(13,1) + C(52,3)

I am not sure if this is in any way correct and I am worried I'm going to learn this completely the wrong way. Any advice would be great! Thank you.