Three cards are chosen at random from a standard 52-card deck. What is the probability that they all have different suits?
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Three cards are chosen at random from a standard 52-card deck.
What is the probability that they all have different suits?
52 cards in the deck. The 1st card can be any of them.
51 cards left. The 2nd card has to be one of the 39 that aren't the same suit.
50 cards left. The 3rd card has to be one of the 26 that are neither of the first two suits.
1 x 39/51 x 26/50 = 1014/2550 = 0.3976 round it to 39.8% probability.
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