1985 AJHSME Problem 22

Assume every 7-digit whole number is a possible telephone number except those that begin with 0 or 1. What fraction of telephone numbers begin with 9 and end with 0?

\textbf{(A)}\ \frac{1}{63} \qquad \textbf{(B)}\ \frac{1}{80} \qquad \textbf{(C)}\ \frac{1}{81} \qquad \textbf{(D)}\ \frac{1}{90} \qquad \textbf{(E)}\ \frac{1}{100}

*Note: All telephone numbers are 7-digit whole numbers.*

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