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$\mathcal F \subset 2^X$, where $ X = \{1\ldots n\} $ and $ \forall F_1, F_2 \in \mathcal F$ : |$F_1 \cap F_2 $| $ \neq 0$. I need to find the amount of such $\mathcal F$ such that |$\mathcal F$| = $2^{n-1}$. Can anyone help?

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Do you mean what is the maximum size of such an $\mathcal{F}$? –  André Nicolas Nov 27 '12 at 20:44
    
No, i mean what is the amount of different $\mathcal F$ with given size –  John Smith Nov 27 '12 at 20:50
    
Advice: Try to solve your problem first when $\,n=1,2,3\,$... –  DonAntonio Nov 27 '12 at 20:54

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