Odds of pairs

Pair hands are defined by the rank of the pair, the suit combos and the kicker combos. The number of arranged suit combos are 12. The first (paired) card can be any of the 4 suits, and the second can be any of the remaining 3 suits. The arrangement of the suits doesn't matter, so there are actually 6 suit combos. The first kicker can be any of the 48 cards with a different rank than the pair. The second kicker can be any of the 44 cards that doesn't pair the first kicker or equals the pair in rank. The third kicker can be any of the 40 cards that doesn't pair any of the other kickers or equals the rank of the pair. There are 3*2*1 = 6 different ways to arrange the kickers.

n(pair of ace hands) = suit combos * kicker combos = 6 suit combos * (48*44*40/6) pair of ace hands/suit combo = 84480 pair of ace hands

There are also 84480 pair of king hands, 84480 pair of queen hands and so on.

n(pair hands) = pair combos * suit combos * kicker combos = 13 pairs * 6 suits/pair * 14080 pair hands/suit = 1098240 pair hands