# poker5 - 5 Card Poker Hands(52 Card Deck Possible Hands = 5...

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5 Card Poker Hands (52 Card Deck) Possible Hands: 960 , 598 , 2 )! 5 52 ( ! 5 ! 52 5 52 = - = Royal Flush: {Ace,King,Queen,Jack,10 of same suit}: 4 possible ways Straight Flush: Suppose: Ace,2,3,4,5 of same suit (4 ways). Then cycle through all starting points (Ace,2,…,9) (9 ways) 36 possible ways. 4 of a kind: Suppose 4 aces (5 th card can be any of the remaining 48 (48 ways). Then cycle through all possible numbers (2,3,…,King) (13 ways) 48(13)=624 possible ways Full House (A pair of one number, 3 of the other): Suppose 3 Aces and 2 2’s: ways 24 ) 6 ( 4 2 4 3 4 = = . There are 13(12) permutations of 2 numbers where we get 3 of one and 2 of the other: 24(13)(12)=3744 possible ways Flush (All cards of same suit): Suppose clubs: 1287 5 13 = ways. There are 4 suits 1287(4)=5148 ways. Removing Royal flushes and straight flushes

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poker5 - 5 Card Poker Hands(52 Card Deck Possible Hands = 5...

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