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What is the probability of drawing a full house from a standard 52-card deck of playing cards?
What is the probability of drawing a full house from a standard 52-card deck of playing cards?
If you're asking for the probability of drawing a full house in 5 cards, let's count the number of ways to get a full house and divide by the number of hands:
3 of a kind and 2 of a kind:
13 * (4 choose 3) * 12 * (4 choose 2) = 3744
This gives you 3 of the four cards of one value, and 2 of the four cards of a different value.
The total number of hands is simply 52 choose 5.
So that means the probability is:
P = 3744 / (52 choose 5) = 3,744 / 2,598,960 = 6 / 4165
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