# $\mathcal F\subset 2^{[n]}$ and $\forall F_1, F_2\in\mathcal F : |F1∩F2| \neq0$. What is the amount of $\mathcal F : |\mathcal F| = 2^{n−1}$?

$\mathcal F \subset 2^X$, 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