Pre-Calc, Probability

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From a deck of 52 playing cards, 7 cards are dealt. What are the odds of the following event occuring
--4 From one suit, 3 from another

The probability of the event occurring is also acceptable. But, the answer is 99/16722971 (as far as the odds go

  • Pre-Calc, Probability -

    Could be:
    HHHHCCC
    HHHHSSS
    HHHHDDD

    Now, each of those can be arranged in 7!/(4!3!) or 35 ways

    let' calculate the prob of one of these, HHHHCCC

    Prob(HHHHCCC)
    = (13/52)(12/51)(11/50)(10/49)(13/48)(12/47)(11/46)
    But the same prob is true for all of the 35 cases,
    so multiply that by 35 to get

    prob(4from one suit, 3 from another) = 1573/1029112
    so the prob of NOT any of those = 1 - 1573/1029112
    = 1027539/1029112

    So the odds in favour of 4 from one suit, 3 from another
    = 1573 : 1027539

    check my arithmetic, I did not get the same answer you gave.

  • ARGGHH - error -Pre-Calc, Probability -

    oops, for some reason I read it as
    4 Hearts, 3 from another

    so it could be
    HHHHCCC
    HHHHSSS
    HHHHDDD

    DDDDHHH
    DDDDCCC
    DDDDSSS

    SSSSHHH
    SSSSCCC
    SSSSDDD

    CCCCHHH
    CCCCSSS
    CCCCDDD

    So there are 12 of these and each can be arranged in 35 ways
    so to get the prob of one of these 420 cases, multiply
    (13/52)(12/51)(11/50)(10/49)(13/48)(12/47)(11/46) by 420

    (my calculator is overheating)

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