Probability of n k-sided dice showing exactly m different faces

2010-02-21T19:05:14Z

I found the following closed form solution for the abovementioned problem:

$${1\over k^n}\cdot{k!\over (k-m)!}\cdot{\{{n\over m}\}}$$ with ${\{{n\over m}\}}$ being the Stirling Number of the second kind.

Although it seems to have some intuition and seems to work for a sample problem for which I have the solution this closed form is not from a trusted source. Unfortunately I can't find any other source.

My question: Could anyone acknowledge this closed form solution and/or give me a hint where to find a citable source.

Answer by Kristal Cantwell for Probability of n k-sided dice showing exactly m different faces

2010-02-21T19:31:43Z

Applied probability by Kenneth Lange deals with this problem on page 74. It is on Google books, here is the URL.

Probability of n k-sided dice showing exactly m different faces - MathOverflow

Probability of n k-sided dice showing exactly m different faces

Answer by Kristal Cantwell for Probability of n k-sided dice showing exactly m different faces