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 \neq \emptyset.
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 \neq \emptyset.