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Posers and Puzzles

Posers and Puzzles

  1. Standard member royalchicken
    CHAOS GHOST!!!
    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. Donation richjohnson
    TANSTAAFL
    27 May '03 18:38 / 1 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 member royalchicken
    CHAOS GHOST!!!
    27 May '03 20:22
    Maybe, maybe not. What is your reasoning?
  4. Donation richjohnson
    TANSTAAFL
    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 member royalchicken
    CHAOS GHOST!!!
    28 May '03 01:47 / 1 edit
    I get 27522......Good job ! (My method was different though.)