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There are (52 choose 7) = 133784560 total possible hands in 7 card poker. Of these, 13 * 12 are a "Big Full House." To see why, consider all the seven-card hands with four aces and three of a kind: AAAA222 AAAA666 AAAA101010 AAAA333 AAAA777 AAAAJJJ AAAA444 AAAA888 AAAAQQQ AAAA555 AAAA999 AAAAKKK There are 12 of these hands for each of the 13 ...


p is 0.0000046642 Here are two different ways to arrive at this result... If you have XY, there is one way to make "quad X" and C(3,2) ways to make "set Y". If you have XY, there is also one way to make "quad Y" and C(3,2) ways to make "set X". C(3,2) is 3, so starting from XY, there are 6 possibilities to make what you called the "big full house" (very ...

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