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? Thanks in advance, Woolly Rhino.