Acertain country's postal service currently uses 55-digit zip codes in most areas. how many zip codes are possible if there are no restrictions on the digits used? how many would be possible if the first number could not be 00?

There would be 100,000 if there are no restrictions on the digits and 90,000 if they cannot use 0 as the first digit.

If there are no restrictions, there are 10 possibilities for each digit:
10(10)(10)(10)(10) = 100,000

If the first digit cannot be 0, there are 9 possibilities for it and 10 possibilities for each of the other 4:
9(10)(10)(10)(10) = 90,000