1986 AHSME Problems/Problem 10

Problem

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 $85$ th word in this list is:

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

Solution 1

We could list out all of the possible combinations in dictionary order.

$73rd:$ MAEHS $74th:$ MAESH $75th:$ MAHES $76th:$ MAHSE $77th:$ MASEH $78th:$ MASHE $79th:$ MEAHS $80th:$ MEASH $81th:$ MEHAS $82th:$ MEHSA $83th:$ MESAH $84th:$ MESHA $85th:$ MHAES

We find that the 85th combination ends with the letter S. So the answer is $\textbf{(C)}\ S$ .

1986 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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1986 AHSME Problems/Problem 10

Problem

Solution 1

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