Combination and Permutations

What is the probability that a five-card poker hand has the following?

(a) Two Pairs (not four of a kind or a full house).

Choose a kind - 13

Choose 2 of a kind - C(4,2)

Choose another kind - 12

Choose 2 of a kind - C(4,2)

Choose last card - 44

Multiply all number above for answer.

Is that right?

Another thing that came to mind is to replace the 13 and the 12 by C(13,2), I'm having trouble choosing one over the other. Can somebody confirm the right answer and explain why. Thank you.