How many ways we can divide '$n$' distinct items into $r$ identical groups where a group must have at-least one item?
I am looking for some approach for solving this problem.
How many ways we can divide '$n$' distinct items into $r$ identical groups where a group must have at-least one item?
I am looking for some approach for solving this problem.
Your question is addressed exactly via the Stirling Numbers of the Second Kind. In particular, there is an explicit formula $\left\{\begin{matrix} n \\ r \end{matrix}\right\} = \frac{1}{r!}\sum_{j=0}^{r}(-1)^j{r \choose j} (r-j)^n.$