How many phone numbers are possible for a certain area code Assume that zero cannot start an area code or the first digit of the number itself Which method should be used to solve this problem?

Answer 1

There are some necessary parameters missing in your problem as written above. You need to know, first and foremost, how many digits in a telephone number. In the USA and Canada, that is always 7, but in some countries it may be more or less than that, and some places even have different lengths of telephone numbers within the same city or town, but that would be beyond the scope of this type of word problem.

A digit with no restrictions has ten possible values. The restriction that the first digit cannot be zero reduces that position to 9 possible values. Multiply together the number of possible values for each digit of the telephone number. For example, if you have a 7-digit phone number, and the only restriction is that the first digit cannot be zero, then you have

9 x 10 x 10 x

10 x 10 x 10 x 10 x 10

= 9,000,000 possible telephone numbers

In reality, there are about 7.9 million possible phone numbers in any given US or Canadian area code, because there are additional restrictions on the first three digits. For example, a number can begin with 4, and can even begin with 41, but cannot begin with 411.