MathDB
Count the words!

Source:

January 8, 2005
algorithmfactorial

Problem Statement

The 120 permutations of the AHSME are arranged in dictionary order as if each were an ordinary five-letter word. The last letter of the 85th word in this list is:
<spanclass=′latex−bold′>(A)</span> A<spanclass=′latex−bold′>(B)</span> H<spanclass=′latex−bold′>(C)</span> S<spanclass=′latex−bold′>(D)</span> M<spanclass=′latex−bold′>(E)</span> E <span class='latex-bold'>(A)</span>\ \text{A} \qquad <span class='latex-bold'>(B)</span>\ \text{H} \qquad <span class='latex-bold'>(C)</span>\ \text{S} \qquad <span class='latex-bold'>(D)</span>\ \text{M} \qquad <span class='latex-bold'>(E)</span>\ \text{E}
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