Assuming that the first ball was black, the probability that the second is also black is 4/51. The probability that the first ball is black is 5/52. What is the probability that all 5 balls drawn are black? Imagine having a urn with 52 balls, of which 5 are black and the remaining white. shows another elegant way of arriving at the same probability. The probability of whichever hand is naturally 1/2598960. The poker sample space consists of 2598960 equally probable elementary events. Thus there are C(52, 5) = 2598960 different hands. The product 52×51×50×49×48 must be divided by 5! because the order in which the five cards are added to the hand is of no importance, e.g., 7♣8♣9♣10♣J♣ is the same hand as 9♣7♣10♣J♣8♣. There are C(52, 5) possible combinations of 5 cards selected from a deck of 52: 52 cards to choose the first of the five from, 51 cards to choose the second one. Poker uses the standard deck of 52 cards. Below, we shall evaluate probabilities of several hand combinations. The hands are compared according to a predetermined ranking system. Common to all is the fact that players get - one way or another - hands of five cards each.
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