Two cards are drawn from a pack of 52 cards. what is the probability that both of the same suit

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So, I am having a problem with this in that the method I use gives two completely separate answers.

Two cards are selected from a deck of $52$ playing cards. What is the probability they constitute a pair (that is, that they are of the same denomination)?

So, for the first method I reason this.

The first card picked has a $13/52$ chance of being in some suit. The second card picked has probability $12/51$ of being in the same suit.

So... The probability should be $(13/52)(12/52) = 3/52$.

The other method is by combinatorics.

I have $52 \cdot 51$ one ways of creating a pair of cards. But I have $13 \cdot 12$ different ways of creating a pair of the same suit. Now to me, the logical thing to do is to multiply this number by $4$, because I would have to count each valid pair from each suit.

This would give me

$$\frac{4 \cdot 12 \cdot 13}{52 \cdot 51}$$

What's wrong with the reasoning on the second one?