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Question: the game of thirtyone has threecard hands the score of...

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The game of thirty-one has three-card hands; the score of a hand is equal to the highest sum of cards within a single suit, where face cards (Jack / Queen/ King) count as 10 and Aces as 11. (So the hand K♠, Q♦, 5♠ would be worth 15, the value of the spades in the hand; 9♥, 8♥, 4♥ would be worth 21.)

(a) How many hands are there worth 30 or more points?

(b) Which is more common: drawing a hand that is worth 31 points, or drawing three cards of the same rank?

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