2009-3 Intersecting family

Let \(\mathcal F\) be a collection of subsets (of size r) of a finite set E such that \(X\cap Y\neq\emptyset\) for all \(X, Y\in \mathcal F\). Prove that there exists a subset S of E such that \(|S|\le (2r-1)\binom{2r-3}{r-1}\) and \(X\cap Y\cap S\neq\emptyset\) for all \(X,Y\in\mathcal F\).

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