Odds of trips

I define trip hands by the suit combos, the rank of the trips and the kicker combos. The suit combos are most easily defined by the suit of the card you would need to make quads, so there are four suit combos. The kickers have to be of different ranks, both of them different from the rank of the trips. There are 48 cards that meet this requirement for the first kicker, and 44 for the second kicker. If you multiply these numbers, you get the number of arranged kicker combos. The arrangement doesn't matter, so the number of kicker combos are half as big as the number of arranged kicker combos.

n(trip ace hands) = suit combos * kicker combos = 4 suits * (48*44/2) trip ace hands/suit = 4224 trip ace hands

There are also 4224 trip king hands, 4224 trip queen hands and so on.

n(trip hands) = trip combos * suit combos * kicker combos = 13 trips * 4 suits/trip * 1056 trip hands/suit = 54912 trip hands