Question

Kathy just discovered that the telephone company just instituted a new area code for certain districts in Idaho. She also found out that area codes and local numbers cannot begin with 0 or 1. How many different telephone numbers are possible? (Include the area code as part of the phone number.)

Answer 1

The phone number = Area code ( 3 digits) + Local number (7 digits)

Restriction : Area code and Local number cannot begin with 0 or 1.

The telephone number has 10 total digits. Each digit has a choice of being filled by 10 numbers : 0,1,2,3,4,5,6,7,8,9.

EXCEPT the first digit of the area code and local number have only 8 choices : 2,3,4,5,6,7,8,9.

Thus, the total number of different telephone numbers are = 8¹⁰ x 2⁸ = 274,877,906,944

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