Re: A Question on Balls and Bins

On 16 Mar, 17:48, nivekkos...@xxxxxxxxx wrote:
Here's a seemingly simple question about balls and bins that I've been
struggling with. I'm hoping someone can help shed some light on this
problem:

Given k balls with m BLUE balls and (m-k) RED balls. Toss them
independently and uniformly at random into n bins. What is the
probability that there are no bins with both a BLUE and a RED ball?

I can express the probability as an messy sum involving Stirling
numbers of the second kind. But I can't seem to simplify it any
further. Is there a nice way to count things to yield a nice
expression at the end? Or is there an easy way to (non-trivially)
bound this probability?

Thanks.

I think there's a mistake .
(m - k ) RED BALLS ?

.

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