7.) 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. (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?
7.) 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.
(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?
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