How many 10-digit telephone numbers (area code + number)are possible if the first digit cannot be zero, the first three digits cannot be 800 or 900, and the number must end in 0000?
A)900,000
B)898,000
C)654,642
D)899,000

Question

Quizplus · Accepted Answer

The first digit can be any digit from 1 to 9 (9 options), the next two digits can be any digit from 0 to 9 (10 options each), but we must exclude the combinations that form 800 and 900, which are 2 out of 1000 possible combinations for the first three digits. So, for the first three digits, we have 9 * 10 * 10 - 2 = 898 options. The next six digits are fixed as the number must end in 0000, leaving us with 898 * 1 = 898,000 possible telephone numbers.

How Many 10-Digit Telephone Numbers (Area Code + Number)are Possible