AMC 8 2015 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? $\textbf{(A)}\text{ 1} \textbf{(B)}\text{ 2} \textbf{(C)}\text{ 3} \textbf{(D)}\text{ 5} \textbf{(E)}\text{ 6}$