A poker hand consists of five cards from a standard 52 card deck with four suits and thirteen values in each suit; the order of the cards in a hand is irrelevant. How many hands consist of 2 cards with one value and 3 cards of another value (a full house)? How many consist of 5 cards from the same suit (a flush)
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Step-by-step explanation:
First, we have 4C3 choices for removing cards. That is we have 4 choices for removing the same value 3 cards. Now for the pair, we have 4C2 choices, that is we have 6 choices. Now, for removing the three cards we have 13 choices ( 13 cards of different values) and for the remaining pair we have 12 choices. So, in total, the number of hands is 4*6*13*12=3744.
Now for flush, we have 4 different card types so we have four different choices to choose from. And for the cards, we have 13C5=1287. So in total we have 1287*4=5148 choices for a flush
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