AMC 8 1990 Problem 12

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