In the game of blackjack played with one deck, a player is initially dealt two cards. Find the number of different two card initial hands.

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William Delaney | (Level 3) Distinguished Educator

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I believe this question is confusing. Is this about cards or about hands? For example, a jack and an eight is no different from a queen and an eight as far as hand values are concerned. Both add up to eighteen, which is all that matters in blackjack. I believe there are only 55 possible two-card hands. If one card is an ace, then the only combinations are with ace, 2, 3, 4, 5, 6, 7, 8, 9, and any card valued at ten, including any jack, queen, or king. Whether it might be a king of hearts or a king of spades makes no difference. If one card is an ace there are only ten possible hands--ace and two, ace and three, etc. If one card is a two, there are only nine possible additional hands, because two and ace is already covered by ace and two. So I believe you could add ten, nine, eight, seven, six, five, four, three, two and one to get the total number of possible hands. If one card has the value of ten, the only combination not covered in the other calculations would be another card worth ten, which could be a ten, jack, queen, or king of any suit. But this is if we're talking about hands and not just combinations of two cards.

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