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. 

Any suggestions or help please.
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