# Math 217

Topics: Telephone numbers, Toll-free telephone number, North American Numbering Plan Pages: 2 (475 words) Published: December 3, 2011
Amy Letcher
MAT217
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1. A. There are 8 service codes such as: 211, 311, 411, 511, 611, 711, 811, and 911.

B. There are 72 total ERC (not including service codes). 8 * 10 = 80 – 8 = 72 service codes. The 8 represents the service codes multiplied by the 10 digit number then I subtracted the 8 service codes since it was not including them.

C. There are 5 toll free numbers such as: 800, 855, 866, 877, and 888.

D. There are 50,000,000 toll free phone numbers (without restrictions). I multiplied the 5 toll free numbers by 10 to the 7th power, since there is no restrictions on the number with 10 digits then raised to the 7th power because of the 7 digit phone number.

2. There are 144 area codes that were available prior to 1995. 8*2*10=160-16=144. I multiplied 8 for the service codes by 2 for the 0 and 1, by 10 for the digits. Then subtracted 16 for codes prior to 1995.

3. There are 656 additional area codes that became available after the middle digit restrictions were removed. 8*10*10=800-144=656. I multiplied 8 for the service codes by 10 for the middle number since it opened up, then by 10 for the digits which equaled 800, then subtracted the 144 that was already available found in answer 2.

4. If you make 0 and 1 available it would increase the available number of phone numbers by 344. 10*10*10=1000-656=344. I took the 10 for the first set in a number and multiplied it by 10 for the middle numbers, then by 10 for the last set of numbers and got 1,000. Then subtracted the 656 additional area codes that became available.

5. There are 8,000,000 phone numbers available in each area code of TV land. 800*1*1*1*10*10*10*10=8,000,000. I multiplied 8 for the service codes by 10 for the middle number since it opened up, then by 10 for the digits which equaled 800. Then multiplied that by 1*1*1 representing the “555”, then multiplied that by 10*10*10*10 representing the last 4 digits of the phone number.

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