How many ways can 12 cards be chosen from a standard deck of 52 cards such that the same number of cards from each suit are in the 12?

The way I saw it was that initially, you had to chose 1 of the 4 suits, i.e., . Then within the chosen suit you needed to choose 3 cards, i.e., , then repeat the process with the remaining 3 suits, so my solution was:

The answer provided says:

Why is the choice of suit not included?