Of the 52 cards in the deck, four are aces and others (kings, queens, jacks, and tens) are worth 10 points each. The dealer has a blackjack if one card is an ace and the other is worth 10 points; it doesn't matter which card is face up and which card is face down. How many different blackjack hands are there?

64 different black jack hands

Step-by-step explanation:

there are 4 aces in a deck, and you can score a blackjack if any of these 4 aces is paired with any of the 16 different cards that are worth 10 points. Total number of different blackjack combinations = 4 aces x 16 different tens = 64.

Even though the number of possible blackjack hands might seem large, the possibilities of actually getting one are really low:

possibility of getting 1 ace = 4/52 = 1/13

possibility of getting 1 ten = 16/51

possibility of getting a blackjack = 16 / 663

if you start with the 10 first the odds are the same:

possibility of getting 1 ten = 16/52 = 4/13

possibility of getting 1 ace = 4/51

possibility of getting a blackjack = 16 / 663

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