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Let number of elements in a set be $1,2,3...n^2$ , for a given "n" . I want to know the number of subsets having "n" elements such that any two sub-sets have atmost one element in common.

Example: For $n=2$, we have $\{1,2,3,4\}$ in the set. And number of subsets satisfying the above criteria is $\{1,2\}, \{3,4\}, \{1,3\},\{1,4\},\{2,4\},\{2,3\}$.

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    This is a variant on the Kirkman schoolgirls problem, which see.2012-05-29

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