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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.

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

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