Current rules for telephone area codes allow the use of digits \( 2-9 \) for the first digit, and \( 0-9 \) for the second and third digits, but the last two digits can as 911 ). How many different area codes are possible with these rules? That same rule applies to the exchange numbers, which are the three digits Given both of those rules, how many 10 -digit phone numbers are possible? Given that these rules apply to the United States and Canada and a feu (Assume that the combined population is about \( 400,000,000 \).) How many possible area codes are there? (Type a whole number.)

To determine how many different area codes are possible under the given rules, we consider each digit's allowed values: 1. The first digit of the area code can be any digit from \( 2-9 \), giving us \( 8 \) options. 2. The second and third digits can each be any digit from \( 0-9 \), giving us \( 10 \) options for each of them. Therefore, the total number of possible area codes can be calculated as: \[ 8 \times 10 \times 10 = 800 \] So, there are \( 800 \) possible area codes. Now, let's determine how many different 10-digit phone numbers are possible. A 10-digit phone number consists of an area code (3 digits) followed by an exchange number (3 digits), and then a line number (4 digits). 1. Area Code: \( 800 \) options (as calculated above). 2. Exchange Number: The first digit can again be \( 2-9 \) (8 options), and the next two digits can be \( 0-9 \) (10 options each): \[ 8 \times 10 \times 10 = 800 \] 3. Line Number: Each of the 4 digits can be \( 0-9 \) (10 options each): \[ 10 \times 10 \times 10 \times 10 = 10,000 \] To find the total number of possible 10-digit phone numbers, we multiply the options for each part together: \[ 800 \text{ (area codes)} \times 800 \text{ (exchange numbers)} \times 10,000 \text{ (line numbers)} = 6,400,000,000 \] Thus, the total number of possible 10-digit phone numbers is \( 6,400,000,000 \).