Five cards are dealt from a standard 52-card deck. What is the probability that we draw a “full house” (3 cards of one kind, 2 cards of another kind)?

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Geraldine Flores · Accepted Answer

Total number of ways of selecting 5 cards from 52 is  (525)=2,598,960  First of all, notice that we have 13 kinds of cards.  From that, we need to choose 2 kinds such that one kind we will have 2 cars  Number of ways to choose these 2 kinds from 13 and order them is 2×(132)=156  Now, the number of ways in which we can have 3 cars of a particular kind and 2 cars of other particular kind is  (43)⋅(42)=24Z  This is because we have 4 cards of each kind.  So, the number of ways to get a full house is 24⋅156=3744. Therefore,  P(getting a full house=37442598960=0.0014406  Result: 37442598960

Five cards are dealt from a standard 52-card deck. What is the probability that

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