Let $r \leq n$.
I know that the number of ways of grouping $n$ labeled objects in $r$ non-empty unlabeled groups is given by $S(n,r)$. (Stirling's number of 2nd kind)
But, also the number of ways of grouping $n$ labeled objects in $r$ non-empty labeled groups is given by $n! \cdot C(n-1,r-1)$ (stars and bars problem). Then why isn't the number of ways of grouping $n$ labeled objects in $r$ non-empty unlabeled groups equal to $\frac{1}{r!}[n! \cdot C(n-1,r-1)]$, by the latter formula?