# Tagged Questions

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### Stirling's approximation to birthday problem

a) What is the probability that in a group of N people, at least two share a birthday? Solved. P = 1 - 365!/[(365)^n. (365-n)! b) Use Stirling's approximation Ln (n!) = n ln(n) - n for large n to ...
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### Bins and balls model - filling first bins [close]

We have $n$ bins and $m$ balls. I want to compute the probability that in the first $k$ bins, $q$ of them will be non-empty. I can throw $m$ balls into $n$ bins in $n^m$ ways. Using Stirling ...
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### Number of Singleton Blocks in Set Partition

I'm interested in some general information on the following question: Consider the collection of partitions of an $n$-set into $m$ blocks as a uniform probability space. Let $X$ be the random ...
I am interested in making a certain statement on the probability distribution of "drawing a sample with $d$ distinct elements, when the sample is of size $k$ and is drawn (with replacement) from a set ...