-2
votes
1answer
70 views

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 ...
2
votes
1answer
116 views

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 ...
0
votes
0answers
39 views

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 ...
0
votes
1answer
110 views

Proving a statement on the probabilty of “Drawing distinct items”

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 ...
2
votes
1answer
123 views

Probability of finding exactly $m$ cells empty

Another problem on combinatorics. This time I'm asking for a hint and if it is possible a general strategy when dealing with this kind of problems. Show without using the preceding results * that the ...