## 10 Digit Call

A typical telephone number in the United States used to be $7$ digits. While you can still use a seven-digit code in most areas, a multitude of regions have begun using ten-digit telephone numbers. If the entire country goes to a ten-digit telephone, exactly how many different ten-digit telephone numbers will be available such that the first digit cannot be a $0$ or $1$ and the fourth digit cannot be a $0$ or a $1$?
Source: mathcontest.olemiss.edu 11/11/2013

SOLUTION
There are $8$ choices $\left\{2,3,4,\cdots,9\right\}$ for the first digit and $8$ choices $\left\{2,3,4,\cdots,9\right\}$ for the fourth digit. For all other digits, there are $10$ choices $\left\{0,1,2,\cdots,9\right\}$.
Total choices
$8\times 10\times 10\times 8\times 10\times 10\times 10\times 10\times 10\times 10=64\times 10^8$ different ten-digit telephone numbers.

Answer: $64\times 10^8$