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Math Help - a hand of 13 cards ...

  1. #1
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    a hand of 13 cards ...

    a hand of 13 cards are chosen at random from a deck of 52 playing cards. What is the probability that a hand is void in at least one suit.

    Hint: Note that the answer is not (4 1)(39 13) / (52 13)

    Thank you so much
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sabrina87 View Post
    a hand of 13 cards are chosen at random from a deck of 52 playing cards. What is the probability that a hand is void in at least one suit.

    Hint: Note that the answer is not (4 1)(39 13) / (52 13)

    Thank you so much
    Well, lets do the calculation for void in hearts.

    The number of ways of selecting a hand of 13 cards void in hearts is 39 \times 38 \times ... \times 27 =\frac{39!}{26!}<br />
(we can divide by 13! if we wish to not distinguish between permutations, but we don't need to here)

    So the number of ways of selecting a hand void in some suit is 4 \times \frac{39!}{26!}

    The total number of hands is \frac{52!}{39!}

    The probability you seek is the ratio of these.

    CB
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