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

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About mvtrinh

Retired high school math teacher.
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