1986 AHSME Problem 10

The 120 permutations of AHSME are arranged in dictionary order as if each were an ordinary five-letter word. The last letter of the 86th word in this list is:

\textbf{(A)}\ \text{A} \qquad \textbf{(B)}\ \text{H} \qquad \textbf{(C)}\ \text{S} \qquad \textbf{(D)}\ \text{M}\qquad \textbf{(E)}\ \text{E}

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