<p> </p> <p>Find the number of collections of <img alt="$16$" height="14" src="https://latex.artofproblemsolving.com/9/a/5/9a5b4928c8fe50ce3c2428da3bee3505e891b788.png" width="20" /> distinct subsets of <img alt="$\{1,2,3,4,5\}$" height="20" src="https://latex.artofproblemsolving.com/d/2/2/d2289231163b75dca0daf0f842ee0fba6f289fc2.png" width="98" /> with the property that for any two subsets <img alt="$X$" height="14" src="https://latex.artofproblemsolving.com/6/a/4/6a47ca0fe7cb276abc022af6ac88ddae1a9d6894.png" width="18" /> and <img alt="$Y$" height="14" src="https://latex.artofproblemsolving.com/c/e/5/ce58e4af225c93d08606c26554caaa5ae32edeba.png" width="16" /> in the collection, <img alt="$X \cap Y \not= \emptyset.$" height="19" src="https://latex.artofproblemsolving.com/a/5/d/a5d0df951b998a7931ac51b1cab9659e2ca001a8.png" width="92" /></p>

Question No: 450

Find the number of collections of $16$ distinct subsets of $\{1,2,3,4,5\}$ with the property that for any two subsets $X$ and $Y$ in the collection, $X \cap Y \not= \emptyset.$

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Tags: Combinatorics

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