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) 898,000
B) 654,642
C) 900,000
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. Since there are 100 combinations for each of the next two digits (10x10), and we exclude 2 (800 and 900), we have 98 options for the first three digits. The next six digits are fixed as the number must end in 0000, leaving us with 9 (for the first digit) * 98 (for the next two digits) * 1 (since the last four digits are fixed as 0000) = 882 options for the first three digits. However, since the question asks for 10-digit telephone numbers and the last four are fixed, we actually calculate for the first six digits, which was incorrectly approached in the initial explanation. Correctly, for the first three digits, considering the restrictions, we have 9 options for the first digit, 10 for the second, and 10 for the third, minus the 2 restricted combinations, giving us 9*10*10 - 2*9 = 900 - 18 = 882 combinations. This error in calculation led to a misunderstanding of the problem's requirements. The correct approach should consider the structure of the telephone number and the specific restrictions given, leading to a calculation that accurately reflects the number of possible combinations given the constraints on the first three digits and the fixed ending.

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