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There are (52 choose 7) = 133784560 total possible hands in 7 card poker. Of these, 12 * 4 * 13 are a "Big Full House." To see why, consider the 12 seven-card hands with four aces and three of a kind, disregarding suit: AAAA222 AAAA666 AAAA101010 AAAA333 AAAA777 AAAAJJJ AAAA444 AAAA888 AAAAQQQ AAAA555 AAAA999 AAAAKKK For each of these 12 hands, ...


p is 0.0000046642 Here are two different ways to arrive at that 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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