partitioning in a number of groups

Someone know how to compute in how many ways is it possible to partition a collection of $\displaystyle M$ indistinguishable elements in $\displaystyle I$ groups (evidently with at least one element for each groups)???

The groups are distinguishable; I mean, if $\displaystyle M=3$ and $\displaystyle I=2$ the solution is 2 combinations (1,2) and (2,1) (whereas (3,0) and (0,3) are not allowed since a group is empty)

( probably related to this thread

http://www.mathhelpforum.com/math-he...subgroups.html )