A full house hand consists of trips of a certain rank, and a pair of a different rank. I have already stated the parameters that define trips and pairs. When you have a full house, there are no kickers so you ignore kicker combos. Trip aces and a pair is called aces full, trip kings with a pair is called kings full and so on.
n(aces full hands) = suit combos(trips) * pair combos * suit combos(pair) = 4 suits * 12 pairs/suit * 6 aces full hands/pair = 288 aces full hands
There are also 288 kings full hands, 288 queen full hands and so on.
n(full house hands) = trip combos * suit combos(trips) * pair combos * suit combos(pair) = 13 trips * 4 suits/trip * 12 pairs/suit * 6 full house hands/pair = 3744 full house hands
NB: Once you have trips of a certain rank, you can't have an additional pair of the same rank. There are only 12 possible pairs for a certain category (jacks full for instance) of full house hands.
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