Phone numbers are 10 digits long. How many possible phone numbers are there if the 1^st and 4^th numbers can't be 0?

• A. $10$
• B. $90$
• C. $8,100,000,000$
• D. $10,000,000,000$

Answer: (C)

Verified step by step guidance

1. Understand that a phone number is a sequence of 10 digits, where each digit can range from 0 to 9.
2. Identify the constraints: the 1st and 4th digits cannot be 0. This means for these positions, the digits can range from 1 to 9.
3. Calculate the number of possibilities for the 1st digit. Since it cannot be 0, there are 9 possible choices (1 through 9).
4. Calculate the number of possibilities for the 4th digit. Similarly, since it cannot be 0, there are 9 possible choices (1 through 9).
5. Calculate the number of possibilities for the remaining 8 digits (2nd, 3rd, 5th, 6th, 7th, 8th, 9th, and 10th). Each of these can be any digit from 0 to 9, giving 10 possible choices for each. Multiply the possibilities for each digit position to find the total number of possible phone numbers.