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### Total of Possible Telephone Numbers

```
Date: 1/23/96 at 11:2:28
From: Anonymous
Subject: Permutation of Tel. Numbers

Try to determine the total possible telephone numbers in the U.S.
using the following: Area codes are three digits in which the
middle digit is either 0 or 1 and the first digit can be anything but
0 or 1. No three exchange digits can be the same as the preceding
area code.

Thanks.
```

```
Date: 3/11/96 at 21:33:22
From: Doctor Patrick
Subject: Re: Permutation of Tel. Numbers

Hi!  The easiest way to solve this problem is to break it up into
parts.

Let's start with the area code.  The first digit has 8 possible
numbers (2-9), the second digit has only 2 numbers (0 and 1) and
the third can be all ten numbers (0-9). This gives us a total of
8*2*10, or 160 area codes.

Each area code is followed by a three-digit number that can't
equal the area code.  Three digits from 0-9 gives us 10^3, or
1000, possible numbers and we have to subtract 1 for the number
equal to the area code, leaving us with 999 possible combinations
to follow each of the 160 possible area codes.  So far that gives us
160*999 different combinations, bringing our total to 159840.
Now the last four numbers are easy - since there are no rules
about them it is simply 10^4, or 10000, possibilities.

This makes the total 160*999*10000 different numbers since each
of the 159840 combinations of area codes and three digit numbers
will be followed by 10000 more possible numbers.

-Doctor Patrick, The Math Forum

```
Associated Topics:
High School Permutations and Combinations

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