We calculate the probability of a flush of spades by dividing the number of possible spade flush hands by the number of all possible 5-card hands.ġ,277 / 2,598,960 = 0.00049135 OR 0. So, there are really 1,287 - 10 = 1,277 possible flushes in spades. The question probably wants you to exclude the straight flushes from the probability of ordinary flushes. There are 10 possible straight flushes in spades. However, this includes the possible straight flushes in spades (this is a hand of all spades that are also in consecutive order, e.g. You could consider this the number of possible flushes of spades. There are 1,287 possible hands that are all spades. Now we need to find the probability of getting a flush in spades. This means if you were to make every possible 7 card hand, there would be only 2,598,960 unique combinations. Of those hands, only 2,598,960 are distinct. There are 6,169,740 possible 7 card poker hands. This number is the same for hands of all hearts, diamonds, and clubs. The number of ways that this can be done is called the number of combinations and is denoted with a big c. So, there are 1,287 possible hands that are all spades. Using the combination formula, we will choose 5 cards from the 13 spades: We need to know the number of ways to create hands of 5 cards that are all spades. Note that a deck of cards has the same number of spades, hearts, diamonds, and clubs, so once we find the number of different hands that are all spades, we know the answer for the rest of the suits. I'm assuming from the question that a hand consists of five cards.
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