Question 9
Find the number of four-element subsets of $\{1, 2, 3, 4, \ldots, 20\}$ with the property that two distinct elements of the subset have a sum of $16,$ and two distinct elements of the subset have a sum of $24.$ For example, $\{3, 5, 13, 19\}$ and $\{6, 10, 20, 18\}$ are two such subsets.