Total of Possible Telephone NumbersDate: 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 |
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