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A tarot deck consists of 78 cards. There are 14 cards in each of 4 suits (comprising the usual 13 ranks and a face card called a knight), and there are 21 picture cards and a joker. The picture cards and the joker do not belong to any suit.

A tarot hand consists of 18 cards drawn at random from the deck. What is the probability that a tarot hand has a void, meaning that at least one suit is not present among the 18 cards?

 Mar 24, 2021
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The probability is (C(64,18) + C(50,18) + C(36,18) + C(22,18))/C(78,18), which works out to 1.7%.

 Mar 24, 2021

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