--- James Propp <propp@math.wisc.edu> wrote:
For a change of pace, here's a real probability question: Cheng Qian,
an engineering student doing work on visual sensor networks, asks:
I throw n coins into m barrels randomly. (For a single coin, each barrel has same chance to get it.) Then I count the number of coins in each barrel, say k(i), i=1...m .
My question: what is the probability that all the barrels have no more than K coins, i.e. k(i)<=K, for i=1..m.
Does anyone know any good off-the-shelf approximations to this? (I assume that an exact formula would be too much to ask for.)
This isn't exactly "fun" math, but it's a simple and natural enough question that I thought it wouldn't be out of place in this group.
Jim Propp
An exact solution, that may or may not be useful, is n! C ---- m^n where C is the coefficient of x^n in (sum(x^k/k!, k=0..K))^m. Gene __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com