Probability

The answer is 1 in 694.

Recall that there are 13*4=52 different possible triples in a deck of 52 cards. For each triple, there are 52-4=48 possible candidates for the fourth card (since the fourth card in the triple would make it a four of a kind, and we don't want that). Once you've chosen a fourth card, there are only 3 candidates for the fifth card if you want a full house, since you need one of the 3 remaining cards of the same rank. And there are 2 ways of ordering the two cards, so the number of possible full house variations upon each triple is 48*3/2!=72. Therefore, there are 52*72=3744 possible full house combinations that can be drawn from a 52 card deck, which in turn has 2598960 possible combinations. That is 1 in 694.

card 1 card 2 card 3 card 4 card 5

Just for fun, feel free to click on the cards to see the various possible combinations.

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