Kevin, if you have 4 groups of 13 different cards, then pull out all 4 10's, there are just 12 different ones remaining, correct?

2 2 2 2
3 3 3 3
4 4 4 4
. . . .
A A A A

OK, now I am going to remove 1, then remove another exactly like it.

Surely there are 12 sets of matching cards to start with. And, even after I draw 1 card, there are still 12 identical sets. One set will only have 3 cards, but that does not matter.

Now, there are 11 of the same sets with 4 cards, and one set of cards only has 2.

I know I am not drawing from the set that has 2, or I will have another pair.

That means I am drawing from one of the 11.

Etc.