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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.

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    So, if you say "identical group" you mean "group consisting of identical elements"?2011-11-07

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Your question is addressed exactly via the Stirling Numbers of the Second Kind. In particular, there is an explicit formula $\left\{\begin{matrix} n \\ r \end{matrix}\right\} = \frac{1}{r!}\sum_{j=0}^{r}(-1)^j{r \choose j} (r-j)^n.$

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    and if the groups are also distinct then we have to just multiply this with $r!$ which is $r! \times \left\{\begin{matrix} n \\ r \end{matrix}\right\}$2011-11-07