How many exchanges are needed to serve a city of 80,000 people?

Click For Summary
SUMMARY

To serve a city of 80,000 people, a minimum of 8 exchanges is required, assuming each exchange can accommodate 10,000 unique phone numbers. The calculation is based on the structure of seven-digit phone numbers in the United States, which consist of a three-digit exchange followed by a four-digit number. Given that the first digit of the exchange cannot be 0 or 1, the total number of usable exchanges is limited, necessitating the use of combination and permutation principles to determine the exact number needed for larger populations.

PREREQUISITES
  • Understanding of seven-digit phone number structure in the United States
  • Basic knowledge of combination and permutation mathematics
  • Familiarity with the concept of area codes and exchanges
  • Ability to perform calculations involving large numbers
NEXT STEPS
  • Research the mathematical principles of combination and permutation
  • Explore the structure and allocation of area codes in telecommunications
  • Learn about the limitations of phone number assignments in the U.S.
  • Investigate how population density affects phone number distribution
USEFUL FOR

Mathematicians, telecommunications professionals, urban planners, and anyone interested in the logistics of phone number allocation in populated areas.

Curtiskr
Messages
1
Reaction score
0
A seven-digit phone number in the United States consists of a three-digit exchange followed by a four-digit number. How many exchanges are needed to serve a city of 80,000 people?


Combination, Permutation, and arrangement with repetition equations are used in this section.

Part 1 of this question I got right: 8,000,000 people can have phone numbers in one area code if the first digit of the 7 numbers can't be 0 or 1. Part 2 listed above I'm absolutely stumped on though.
 
Physics news on Phys.org
10,000 numbers per exchange?
 

Similar threads

How many combinations? (High school math problem)
  • · Replies 20 ·
Replies
20
Views
2K
Optimal Itinerary Planning for a Business Trip to Six Major Cities
  • · Replies 2 ·
Replies
2
Views
5K
MHB The Telephone Numbering Plan in North America: Counting Possible Numbers
  • · Replies 4 ·
Replies
4
Views
7K
MHB How Many 3-Digit Even Numbers Can Be Formed from Digits 0-6 Without Repetition?
  • · Replies 7 ·
Replies
7
Views
9K
How Many Ways Can 11 People Be Seated at Two Round Tables?
  • · Replies 7 ·
Replies
7
Views
2K
Counting Principles and Probability
  • · Replies 1 ·
Replies
1
Views
4K
Program to list specific permutations of 5 digits
  • · Replies 4 ·
Replies
4
Views
3K
Need Help 12 Difficult Math questions i need answered by next friday
  • · Replies 2 ·
Replies
2
Views
6K
What is the Correct Probability of a Student Becoming Chairperson?
  • · Replies 3 ·
Replies
3
Views
2K
Counting problem - how many ways....
  • · Replies 4 ·
Replies
4
Views
4K