In order to find the probability of dealing a full house in a 5 card poker hand, you use the folowing:

(13-choose-1)x(4-choose-3)x(12-choose-1)x(4-choose-2) / (52-choose-5)

But in order to find the probability of dealing 2 pairs, you use the this:

(13-choose-2)x(4-choose-2)x(4-choose-2)x(11-choose-1)(4-choose-1) / (52-choose-5)

What I don't understand is why doesn't the 2 pairs probability method work the same way as the full house method (choosing 1 from 13 then 1 from 12 rather than choosing 2 from the 13 at the start) and work as follows:

(13-choose-1)x(4-choose-2)x(12-choose-1)x(4-choose-2)x(11-choose-1)(4-choose-1) / (52-choose-5)