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Urn Problem

  1. Sep 16, 2010 #1
    Dear all,

    We are trying to compute the number of ways for a computer to execute concurrent processes.
    It appears that this problem is equivalent to asking the following:

    Assume that an urn is filled with different quantities of differently colored balls. There are k different colors, and the number of balls of a given color is denoted nk.
    Balls are drawn from the urn it is empty, and the color of the drawn ball is noted.

    The question is: how many different color sequences can be constructed in this way?

    Thank you,

    Martin
     
  2. jcsd
  3. Sep 16, 2010 #2
    Let N=n1+n2+...+nk

    The answer for your question is
    [tex]
    \frac {N!}{n_1!\dots n_k!}
    [/tex]
    because there would be N! possibilities if the colours were pairwise different, but they are not, so we counted each possibility a lot of times. One can permutate the balls from the jth colour n_j! ways but when doing so we don't see any difference in the colour-sequence, so we have to divide N! by n_1!...n_k!
     
  4. Sep 16, 2010 #3
    Hi csopi,

    Thank you for a quick reply and for a clear and coherent explanation!

    The formula matches our calculations, so I think we have our answer :)

    Best regards,

    Martin
     
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