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## Main Question or Discussion Point

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.

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.

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