So, there is a flaw in my solution. Conceptually it's on the right track. But it doesn't count the cards left in the deck with pairs and without pairs correctly. Which means that some the terms will get more complicated. Complicated in such a way that I don't particularly care to try to fix at this moment. I'll get back to you guys if I do find a good fix. But don't hold your breath.

Probability question

[none]

[none]

---