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(solution) With the rapid growth in the use of cellular phones, the number


With the rapid growth in the use of cellular phones, the number of available phone numbers had to be increased.  This was accomplished by increasing the number of available area codes in the United States.  In this project, you will be investigating area codes and how they have been expanded.

Here are some important facts that you need to know about current area codes:

  • An area code contains 3 digits
  • An area code cannot begin with a 0 or a 1

Use what you have learned about the fundamental counting principle, permutations, and combinations to answer the questions below:

1. When the second and third digits of an area code are the same, that code is called an easily recognizable code (ERC). ERCs designate special services and are generally not used as regular area codes.

        a) How many total ERCs are there?

        b) Service codes are one specific example of an ERC. Service codes are ERCs that end in ?11? (like 911). 

            How many service codes are there?

        c) Toll-free numbers are another specific example of ERCs. Do some research to determine the ERCs that are

            currently used for toll-free numbers and list them.

        d) Assume there are no restrictions on the remaining 7 digits in a phone number. How many total toll-free

            phone numbers are there currently?

 

2. Prior to 1995, all area codes had a 0 or a 1 as the middle digit.

        a) How many ERCs were there prior to 1995?

        b) How many area codes (not including ERCs) were available prior to 1995?

 

3. In 1995, the middle-digit restrictions were removed.

        a) How many area codes (not including ERCs) were available after the middle-digit restrictions were removed?

        b) How many additional area codes (not including ERCs) did the change make available?

 

4. Cell phone usage continues to increase even after the changes in 1995.

       a) What further changes could be made to the area code (other than adding a fourth digit) to increase the

           number of available phone numbers?

        b) How many ERCs would be available after your suggested change?

        c) How many area codes (not including ERCs) would be available after your suggested change?

        d) How many additional area codes (not including ERCs) would be available after your suggested change?

        e) Assume there are no restrictions on the remaining 7 digits in a phone number. How many additionalphone

            numbers would be available after your suggested change?


Project Guidelines

Use what you have learned about counting, the fundamental counting principle, permutations, and combinations to complete this project. You may also have to do some research to answer some of the questions.  You may use the web, but make sure that you are using a reliable source and verifying what you get with multiple sources!

While you may work together to arrive at your answers for this project, everyone should turn in their own individual work for this project. 

Your write up for this project should include:

  • Answers for each question in complete sentences.
  • All math steps used to arrive at your answers to each question.

Remember?

  • All final answers should be in complete sentences.
  • You may type or hand write the assignment, but remember you will be graded on neatness and the professional appearance of your final product as well as the accuracy of your answer!

 


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