2015 AMC 8 Problem 13

How many subsets of two elements can be removed from the set \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\} so that the mean (average) of the remaining numbers is 6?

\textbf{(A)}\text{ 1}\qquad\textbf{(B)}\text{ 2}\qquad\textbf{(C)}\text{ 3}\qquad\textbf{(D)}\text{ 5}\qquad\textbf{(E)}\text{ 6}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.