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.



Probability of n k-sided dice showing exactly m different faces
Applied probability by Kenneth Lange deals with this problem on page 74. It is on Google books, here is the [URL](http://books.google.com/books?id=otp4TDnz6FwC&pg=PA74&lpg=PA74&dq=Stirling+Number+of+the+second+kind+dice&source=bl&ots=YHHbtcknAO&sig=sGd1_d1UXtlNkWGYINVZH6Tadu0&hl=en&ei=boiBS-CpDImKsgOq6en5Aw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBMQ6AEwAzgK#v=onepage&q=Stirling%2520Number%2520of%2520the%2520second%2520kind%2520dice&f=false).


