simple question on POKER HAND probiblity {full house} So I have a question about the probability of having a full house in a poker hands (5 cards), from a standard deck of cards (52). 
The solution is   
13C1 x 12C1  x [4C3 x 4C2]   x 1/(52C5) 

For 4C3 x4C2, I understand what it means. 
For the first term: 13C1 x 12C1, does this multiplication assumes the ordering such that Kings, Ace in this order is different from Ace, King?
if that is the case, should we also divide 2! to make to not order dependent????

Pick the rank that appears as triple: $13\choose 1$
Pick a different rank that appears as pair: $12\choose 1$
Pick the three suits that occur in the triple: $4\choose 3$
Picj the two colours that occur in the pair: $4\choose 2$.
Note that full house with three aces and two kings is different from three kings and two aces.
