1997 AHSME Problem 24

A rising number, such as 34689, is a positive integer each digit of which is larger than each of the digits to its left. There are \binom{9}{5} = 126 five-digit rising numbers. When these numbers are arranged from smallest to largest, the 97^{th} number in the list does not contain the digit

\textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8

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