Question

A telephone number has the form NXX-ABC-XXXX. Today N is 2-9, and X is 0-9. However, there are exceptions as 37X and 96X are reserved for future use. Additionally N9X is reserved for expanding the total numbers at a later date. Finally, N11 is reserved for service numbers. How many total area codes are currently available given this information?

Answer 1

The total area codes that are currently available is 692.

Explanation:

The area code is of the form: NXX.

The variable N can take values,

N = {2, 3, 4, 5, 7, 8 and 9}

The variable X can take values,

X = {0, 1, 2, 3, 4, 5, 7, 8 and 9}

Considering that repetitions are allowed.

The total possible number of area codes is:

T = 8 × 10 × 10 = 800

So, there are 800 possible area codes.

The exception codes are:

{37X, 96X, N9X and N11}

• There are 10 possible combinations for 37X.
• There are 10 possible combinations for 96X.
• There are 80 possible combinations for N9X.
• There are 8 possible combinations for N11.

So, the number of reserved area codes is, 10 + 10 + 80 + 8 = 108.

Then the area codes that are currently available is, 800 - 108 = 692

Thus, the total area codes that are currently available is 692.