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Math Help - probability having at least a four seasons

  1. #1
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    probability having at least a four seasons

    Help me!
    We have a deck of cards (52 cards). Assume we draw 13 cards at random. Calculate the probability having at least a form of four seasons (for example, Heart 3, Diamond 2, Club 2, Spade 2). Thanks a lot.
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  2. #2
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    Please be more forthcoming as to what "a form of four seasons " means.
    What exactly does that mean?
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  3. #3
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    It mean a foursome. In a deck of cark, we have 13 foursome. Each foursome consists of four cards of same number. For example, four cards: 9 heart, 9 diamond, 9 club, 9 spade is a foursome.
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  4. #4
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    Quote Originally Posted by mahefo View Post
    It mean a foursome. In a deck of cark, we have 13 foursome. Each foursome consists of four cards of same number. For example, four cards: 9 heart, 9 diamond, 9 club, 9 spade is a foursome.
    Well that is certainly different from the example in the OP.
    There are \sum\limits_{k = 1}^3 {\left( { - 1} \right)^{k - 1} \binom{13}{k}\binom{52 - 4k}{13 - 4k}
    ways to have at least one four of a kind in a deal of thirteen cards from a standard deck.
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