How many end office codes were there pre-1984, when each end office was named by its three-digit area code and the first three digits of the local number? Area codes started with a digit in the range 2-9, had a 0 or 1 as the second digit, and ended with any digit. The first two digits of a local number were always in the range 2-9. The third digit could be any digit.

area code can be 602 but not 134 as first digit should be 2-9 and the second digit should be 0 or 1. So the number of possible area codes were 8 X 2 X 10 = 160.

Similarly for first 3 digits - we have 8 X 8 X 10 = 640 possibilities.

Explanation:

from the information given in the question that area code should start with digit range of digit 2 to 9 and 0 and 1 may be as second digit, while third digit can be any digit. Therefore we have

Take an example - area code can be 602 but not 134 as first digit should be 2-9 and the second digit should be 0 or 1. So the number of possible area codes were 8 X 2 X 10 = 160.

Similarly for first 3 digits - we have 8 X 8 X 10 = 640 possibilities.