Assume every 7-digit [whole number](https://artofproblemsolving.com/wiki/index.php/Whole_number) is a possible telephone number except those that begin with $0$ or $1$.  What [fraction](https://artofproblemsolving.com/wiki/index.php/Fraction) of telephone numbers begin with $9$ and end with $0$?
$\text{(A)}\ \frac{1}{63} \qquad \text{(B)}\ \frac{1}{80} \qquad \text{(C)}\ \frac{1}{81} \qquad \text{(D)}\ \frac{1}{90} \qquad \text{(E)}\ \frac{1}{100}$
Note: All telephone numbers are 7-digit whole numbers.
An equivalent problem is finding the [probability](https://artofproblemsolving.com/wiki/index.php/Probability) that a randomly selected telephone number begins with $9$ and ends with $0$.  
There are $10-2=8$ possibilities for the first digit in total, and only $1$ that works, so the probability the number begins with $9$ is $\frac{1}{8}$
Out of the $10$ possibilities for the last digit, only $1$ works: $(0)$, so the probability the number ends with $0$ is $\frac{1}{10}$
Since these are [independent events](https://artofproblemsolving.com/wiki/index.php?title=Independent_event&action=edit&redlink=1), the probability both happens is \[\frac{1}{8}\cdot \frac{1}{10}=\frac{1}{80}\]
$\boxed{\text{B}}$