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Math Help - choose y balls, how many distinct colors can you get

  1. #1
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    choose y balls, how many distinct colors can you get

    We have y urns of balls. In each urn, we have x balls in the same color. But balls in different urns have difference color.

    Now, without replacement, we draw y balls randomly. What is the chance that we drawn from z different urns or more?

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  2. #2
    Senior Member MacstersUndead's Avatar
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    Let's see. I'll assume there are enough balls in each urn that it can be picked from indefinitely. (that is to say each urn would have y balls)

    If y = 1, then the chance is 0% (trivial, since you can't choose a different urn if you only have one)
    If y = 2, then the possibilities are (let numbers be the colors)
    1 1
    1 2
    2 1
    2 2
    so the probability is 1/2

    If y = 3, then there are 27 possibilities. I counted 18 that weren't all a single color are possible, so the probability would be 2/3.

    At this point, I smell an induction proof, and I'm sure there's an easier way with permutations and combinations.
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  3. #3
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    Hi thanks!!

    We have y urns of balls. In each urn, we have x balls in the same color. But balls in different urns have difference colors.

    Now, without replacement, we draw y balls randomly. What is the chance that we get z(z>=2) different colors or more?
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