An interesting problem in probability

From: Sailesh Kumar (sailesh_at_arl.wustl.edu)
Date: 08/30/04 

Date: Mon, 30 Aug 2004 03:36:07 -0500

Hi,
  I need to do some computation for a cache architecture. I have arrived at
a simplified model and I need help to get it solved. Here is the problem.

  Balls are being put into and removed from a bucket, one arrival and one
departure in each unit time. Balls that are arriving have equal probability
that they can have any color from b different colors.
  The bucket has N balls initially, with equal number of balls of every b
color. N is divisible by b can be assumed. hence N/b balls of each color.

  Now, when this process is carried out for very long time say T (T is
trillions), how many times will the bucket be having balls of only c colors
(c < b).
  In other words, after a long time and in steady state, whats is the
probability that the bucket will have balls of only c colors (c < b).

Thanks in advance,
Regards,
Sailesh

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