1990 AJHSME Problems/Problem 12

Problem

There are twenty-four $4$ -digit numbers that use each of the four digits $2$ , $4$ , $5$ , and $7$ exactly once. Listed in numerical order from smallest to largest, the number in the $17\text{th}$ position in the list is

$\text{(A)}\ 4527 \qquad \text{(B)}\ 5724 \qquad \text{(C)}\ 5742 \qquad \text{(D)}\ 7245 \qquad \text{(E)}\ 7524$

Solution

For each choice of the thousands digit, there are $6$ numbers with that as the thousands digit. Thus, the six smallest are in the two thousands, the next six are in the four thousands, and then we need $5$ more numbers.

We can just list from here: $5247,5274,5427,5472,5724 \rightarrow \boxed{\text{B}}$ .

1990 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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1990 AJHSME Problems/Problem 12

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