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Math Help - Card Probability

  1. #1
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    Card Probability

    "Four cards are drawn from a standard deck. Find the probability that the four cards chosen are dace cards from four different suits." The answer is 81/270725.

    The way I did it was as follows:

    (3C1 x 3C1 x 3C1 x 3C1)/(52C1 x 51C1 x 50C1 x 49C1)

    which resulted in 81/6497400. The numerator is correct, but the denominator is off by a factor of 24! It seems as though I just did the denominator wrong, but I am not sure in what way. I treated it as a dependant event, and if I treate dthem independantly, I would be off by an even larger amount for the denominator, and if I replace each with 13C1, I am too low. I would use the conditional probability forumla, but I only know that for two events, A and B, not four events, A, B, C, and D. I'll try an idea I have in my head, but any suggestions would be welcomed!
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  2. #2
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    The denominator should be { 52 \choose 4}.
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  3. #3
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    Thank, Plato. I thought the dependence of the events would not allow me to do that.
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