The original plan for assigning telephone numbers that you investigated in
Applications Task 4 was implemented in
1947. At that time, the supply of numbers was expected to last for 300 years. However, by the 1970s the numbers were already starting to run out. So, the numbering plan
had to be modified. In this task, you will count the number of different phone numbers that were available in 2012.
a. For three-digit area codes, the first digit cannot be a 0 or a 1. Assuming no additional restrictions, how many three-digit area codes are possible under
this plan?
b. Certain area codes are classified as "Easily Recognizable Codes" (BRCs).
ERCs designate special services, like 888 for toll-free calls. The requirement for an ERC is that the second and third digit of the area code must be the same. The first digit again cannot be a 0 or a 1. How many ERCs are there?
c. Consider the seven digits after the area code. As with the area code, the first digit of the three-digit local prefix cannot be a 0 or a 1. The remaining six digits for the local number have no restrictions. How many of these seven-digit phone numbers are possible?
d. Assuming only the 0 and 1 restrictions in Parts a and c, how many ten-digit phone numbers are possible?