1. Standard memberroyalchicken
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    26 May '03 22:45
    Given a standard, 52-card deck, how many combinations of five cards consist of at least three spades and exactly two cards of equal rank?
  2. Donationrichjohnson
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    27 May '03 18:381 edit
    Originally posted by royalchicken
    Given a standard, 52-card deck, how many combinations of five cards consist of at least three spades and exactly two cards of equal rank?
    31086?
  3. Standard memberroyalchicken
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    27 May '03 20:22
    Maybe, maybe not. What is your reasoning?
  4. Donationrichjohnson
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    27 May '03 23:00
    Originally posted by royalchicken
    Maybe, maybe not. What is your reasoning?
    (1). # of 5-card combos wherein the pair are not one of the 3 spades = (# of distinct 3-spade combos) x (# of distinct non-spade pairs that dont match one of the spades + # of single spade pairs) = 66 x ((39 - 9) + (9x3)) = 3762

    (2). # of combos wherein one of the pair is one of the 3 spades = (# of distinct 3-spade combos) x (# of possibilities for the 4th card for a given set of 3 spades) x (# of possibilities for the 5th card) = 66 x 9 x (48 - (2 (so that the 5th card doesn't match the pair) + 3 + 3 (so that the 5th card doesn't match either of the other two cards)) = 23760.

    (1) + (2) = 27522.

    (my original calculations didn't account for the possible matching of the pair with one of the spades)
  5. Standard memberroyalchicken
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    28 May '03 01:471 edit
    I get 27522......Good job 😀! (My method was different though.)
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