# A Problem in Discrete Probability

1. Oct 3, 2008

### woollyrhino

I recently came across a page named "Gems of Discrete Probability" - http://www.cse.iitd.ernet.in/~sbaswana/Puzzles/Probability/exercises.html

Being a mathematics enthusiast, I tried the first question. Being very rusty in probability, I failed to come up with a satisfying answer: the best I got (for the first question, the expected number of empty bins) was an "open" formula:

n /n\ /n-1\
∑ k * \k/ * \ k /
k=0
----------------------
/2n-1\
\ n /
/n\
Where the notation \k/ is the binomial coefficient, n!/k!(n-k)! .
Is there any way to get rid of the ∑ here, is my solution wrong, is there any way to solve it that will not result in a sum, or is that the best answer?