The telephone company wants to know how many different phone numbers are available for one area code. the only restrictions are on the prefixes, you can't start with a zero and you can't use 411, 611, 811, 911, or 555. how many different phone numbers are available?

Answer 1

phone numbers have to be seven digits, right? 8*9^6

now the three digit phone numbers are not really phone numbers, as they are three digit shortcuts.

Answer 2

In North America, a typical phone number has a 3 digit area code, then a 3 digit number, than a 4 digit number.
e.g. 123 - 456 - 7894

By the "prefix" do you mean the 3 digit number in the middle?
I will assume that.

So number of possible prefixes without restrictions:

= 9x10x10x= 900
excluding the 5 listed above leaves us with 895 possible prefixes.

for each of those, the remaining 4 digit numbers could be 10x10x10x10 = 10,000
So for a given area code, the number of permissible phone numbers
= 895x10000 = 8,950,000