The international telecommunications union (itu) specifies that a telephone number must consist of a coun- try code with between 1 and 3 digits, except that the code 0 is not available for use as a country code, followed by a number with at most 15 digits. how many available possible telephone numbers are there that satisfy these restrictions?

998,999,999,999,999,001 telephone numbers possible

Explanation:

The 0 is not allowed as a country code, but can be part of a country code, like 501 for Belize. So, that means that for the country code, the possible values go from 1 to 999... which represent 999 possibilities.

Then, for each of these country codes, you can have up to 15 digits for the phone numbers.  Most countries use 6 to 12.   The area code is part of the 15-digit phone number.

Since there can be 15 digits, that means that can range from value 1 to value 999,999,999,999,999, for EACH country code.

To get the total number of possibilities, we just have to multiply both numbers together:

999 * 999,999,999,999,999 = 998,999,999,999,999,001 telephone numbers possible.