Answer :
There are total 30 new area codes are possible under new system of telephone companies related to phone numbers with different area codes.
Area codes were introduced in the 1940s. This was an attempt by AT&T to standardize previously disparate numbering schemes.
Originally, area codes were of the form NYX where N=2-9, Y=0-1, X=0-9. N00 and N11 have been excluded. The North American Numbering Plan (NANP) includes 25 countries.
Of the 152 possible area codes, 86 were introduced first. Area codes with 0 in the middle were assigned to states where the area code could cover the entire state. Area codes with 1 in the middle were assigned to states with multiple area codes. The fastest area codes to dial with a rotary phone were assigned to populated areas.
The demand for area codes increased in the 80's and 90's. There were three main factors at the start of this timeframe. 1) the proliferation of cell phones and fax machines, 2) giving Caribbean countries their own area codes rather than sharing the 809 area code, and 3) the US South Pacific joining his NANP. This prompted the industry to increase its stock of area codes by changing the format of both the area code and his CO area code to his NXX. This increased our stock of area codes and CO codes to 792 (8x10x10 - 8 of his N11 codes).
This was a major change that required national coordination.
In 1996, the FCC allowed competition for local communications. This meant that there were many new telecommunications companies with rights to take stock of phone numbers. This has led to a dramatic increase in the demand for numbers and a huge proliferation of new area codes. Over the years, over 30 new area codes have been introduced.
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Complete question:
Several years ago, the US began running out of telephone numbers. Telephone companies
introduced new area codes and numbers were used up, and eventually almost all area codes were
used up. Only answer the questions (c) to (d).
(a) Until recently, all area codes had a 0 or 1 as the middle digit, and the first digit could not be 0
or 1. How many such area codes are possible?
(b) The actual number of area codes under this system was 152. What could be the cause of the
discrepancy between this number and your answer to part (a)?
(c) A 7-digit telephone number that follows the area code cannot start with a 0 or 1. How many
such 7-digit telephone numbers are possible in each area code?
(d) Under the old area code system in part (a), how many total possibilities are there for area
code with telephone number?
(e) The shortage of area codes was resolved by removing the restriction on the second digit of the
area code. (This resulted in problems for some older equipment which used the second digit to
determine that a long-distance call was being made.) How many area codes are possible under
the new system?
(f) How many telephone numbers with area code are possible under the new system?
