<s>[INST] How many possibilities are there for two full houses to be dealt to two players in one game? Imagine dealing cards from a classic 52 card deck to two poker players.
How many possibilities are there for both of them to be dealt a full house(three cards in same rank and two cards of another rank) in same round? 
As I know totally ${13 \choose 1}{4 \choose 3}{12 \choose 1}{4 \choose 2}$ possibilities for one player (AAABB). According to that, I tried to solve my problem as shown below: $${13 \choose 1}{4 \choose 3}{12 \choose 1}{4 \choose 2}{11 \choose 1}{4 \choose 2} + {13 \choose 1}{4 \choose 3}{12 \choose 1}{4 \choose 3}{11 \choose 1}{4 \choose 2}$$ for two players ((AAABB)(AAACC) or (AAABB)(CCCBB)). Is my solution correct or am I missing something?
 [/INST] *

*choose the two three-card ranks. The number  of ways is $\binom{13}{2}\binom{4}{3}\binom{4}{3}$.

*choose a two-card rank. The number of ways is $\binom{11}{1}\binom{4}{2}$.

*the next two-card rank may be the same or different as the first one. The number of ways is $\binom{2}{2}+\binom{10}{1}\binom{4}{2}$

*Take the two players into account, the number of ways is
$$2\binom{13}{2}\binom{4}{3}\binom{4}{3}\binom{11}{1}\binom{4}{2}\left[\binom{2}{2}+\binom{10}{1}\binom{4}{2}\right]$$
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