How many possible 3 digit area codes can be created without repeating a number?
The number of 3-digit numbers with no repeated digits is simply
10x9x8 = 720, if you allow, for example, 012 as a 3-digit
number.
There are 10 digits, any of which might be the first digit. The
second digit can be any digit except the digit that was used for
the first digit, leaving 9 possibilities. The third digit then has
8 possibilities, since it can't be the same as the first or second
digit.
The actual number of possible area codes will be lower, because
there are additional restrictions on the number combinations for a
valid area code. For example, in North America (USA, Canada, etc.),
the first digit of an area code cannot be 0 or 1 and the middle
digit cannot be 9.