What is the probability that a five card poker hand contains

What is the probability that a five card poker hand contains two pairs? (two of each of two different kinds, and a fifth card of a third kind)

Solution :

First choose what the cards in each pair will be: C(13,2) = 78 ways to do this.

Which two cards of each of the kinds of pairs are included: C(4,2) = 6 for each pair.

How many choices for the fifth card (must be different or we have a full house): C(44,1) = 44

Using product rule: 78*6*6*44 ways to have 2 pairs

p(2 pairs) = 78*6*6*44 / C(52,5) = ~ 0.0475