A telephone number has the form NXX-ABC-. 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?

The total area codes that are currently available is 692.

Step-by-step 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}

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.

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step-by-step explanation: