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ihatemath33

  • 3 years ago

a standard 52 card deck of cards is shuffled and then a 12-card hand is dealt from the deck. How many different outcomes are possible that have exactly 3 pairs, and all other cards of different denominations?

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  1. Zarkon
    • 3 years ago
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    I get 53,137,244,160

  2. missgemini92
    • 3 years ago
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    How did you get this?

  3. ihatemath33
    • 3 years ago
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    yes, can you please tell me how you got this. Its right though

  4. Zarkon
    • 3 years ago
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    \[{13 \choose 3}{4\choose 2}^3{10\choose 6}{4\choose 1}^6\]

  5. missgemini92
    • 3 years ago
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    How did you get 10C6 and 4C1*6?

  6. ihatemath33
    • 3 years ago
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    10C6 is because you already chose 3 for the pairs and there is 10 cards left to pick from and then the 6 because you need 6 more cards to make 12 after the three pairs. and the 4C1*6 is for the suit of the remanding 6 cards

  7. Zarkon
    • 3 years ago
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    yes...there are 10 types of cards left over and we want 6 of them. then pick one card from each of these 6 groups

  8. Zarkon
    • 3 years ago
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    note it is (4C1)^6 not 4c1*6

  9. glangdon
    • one year ago
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    I just need a more detailed explanation please

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