Question 168922: How may FIVE card poker hands are there?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How may FIVE card poker hands are there?
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The 1st card can be one of 52, the 2nd will be 1 out of 51, etc, so we get 52*51*50*49*48 = 311,875,200.
But, drawing 3 4 5 6 7 is the same hand as drawing 3 7 5 6 4 (the same 5 cards drawn in a different order), so we have to divide by 5*4*3*2*1 = 5! = 120.
That gives the number of different hands = 2,598,960.
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This is based on the assumption that the same card in a different suit makes a different hand. For example, a full house with 3 Kings, the 10 of Hearts and the 10 of Spades, is viewed as different from a hand with any of the 5 cards exchanged for the same card of a different suit. It has no effect on where it's a winning or losing hand in poker.
Whether this assumption is valid is not specified.
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