Covering by intersecting families (Q1881681)

A family \(\mathcal A\) of \(k\)-element subsets of a finite \(n\)-element set is called intersecting if \(A\cap B\neq\emptyset\) for any \(A,B\in {\mathcal A}\). An intersecting family is called noncentered intersecting if \(\bigcap_{A\in {\mathcal A}} A = \emptyset\). It is proved that for a fixed \(k\geq 3\), the number of noncentered intersecting families to cover the ground \(n\)-set is \({n^2\over 2k(k-1)}(1+O(1/n))\).