Solve the problem.
-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) 899,000
C) 898,000
D) 654,642

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 800 and 900. Since there are 1000 combinations for the first three digits (from 000 to 999) and we exclude 2, we have 998 options for the first three digits. The last four digits are fixed as 0000. The six digits in the middle can be anything from 0 to 9 (10 options each). Therefore, the total number of possible telephone numbers is 998 (for the first three digits) multiplied by $10^6$ (for the six middle digits), which equals 998,000.

Solve the Problem. -How Many 10-Digit Telephone Numbers (Area Code + Number) Are