I would like to calculate the probability of getting two cards but they cant be Kings for example. I thought it could be solved by getting C(48,2) which is 1128. Which means, choose 2 of the remaining 48 cards since I excluded 4 Kings.
But I saw a solution where it gets C(12,2) x C(4,1) x C(4,1) = 1056. Which means get two cards from 12 (13 excluding King) times 4 (kinds of the first card) times 4 (kinds of the second card).
Why these two results are not the same?
The second solution assumes that the face values of the two cards are different, while the first solution doesn't. $C(12,2)$ says "pick two face values out of the pool of $A$ through $Q$." But they must be different.
Add back in the $12$ pairs (with $6$ combinations apiece) and you get the same answer.