Probability of n k-sided dice showing exactly m different faces - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T20:51:08Z http://mathoverflow.net/feeds/question/15981 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/15981/probability-of-n-k-sided-dice-showing-exactly-m-different-faces Probability of n k-sided dice showing exactly m different faces vonjd 2010-02-21T19:05:14Z 2010-02-21T19:32:25Z <p>I found the following closed form solution for the abovementioned problem:</p> <p>$${1\over k^n}\cdot{k!\over (k-m)!}\cdot{\{{n\over m}\}}$$ with ${\{{n\over m}\}}$ being the Stirling Number of the second kind.</p> <p>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.</p> <p><strong>My question</strong>: Could anyone acknowledge this closed form solution and/or give me a hint where to find a citable source.</p> http://mathoverflow.net/questions/15981/probability-of-n-k-sided-dice-showing-exactly-m-different-faces/15983#15983 Answer by Kristal Cantwell for Probability of n k-sided dice showing exactly m different faces Kristal Cantwell 2010-02-21T19:31:43Z 2010-02-21T19:31:43Z <p>Applied probability by Kenneth Lange deals with this problem on page 74. It is on Google books, here is the <a href="http://books.google.com/books?id=otp4TDnz6FwC&amp;pg=PA74&amp;lpg=PA74&amp;dq=Stirling+Number+of+the+second+kind+dice&amp;source=bl&amp;ots=YHHbtcknAO&amp;sig=sGd1%5Fd1UXtlNkWGYINVZH6Tadu0&amp;hl=en&amp;ei=boiBS-CpDImKsgOq6en5Aw&amp;sa=X&amp;oi=book%5Fresult&amp;ct=result&amp;resnum=4&amp;ved=0CBMQ6AEwAzgK#v=onepage&amp;q=Stirling%2520Number%2520of%2520the%2520second%2520kind%2520dice&amp;f=false" rel="nofollow">URL</a>.</p>