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 as 911 . How many different area codes are possible with these rules? That same rule applies to the exchange numbers, which are the three 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 (Assume that the combined population is about \( 400,000,000 \).) How many possible area codes are there? (Type a whole number.)

To solve how many different area codes are possible with the given rules, let's break down the rules: 1. The first digit of the area code can be any digit from 2 to 9. This gives us 8 options (2, 3, 4, 5, 6, 7, 8, 9). 2. The second and third digits can be any digit from 0 to 9, giving us 10 options for each. Now we can calculate the total number of area codes: - Options for the first digit: 8 - Options for the second digit: 10 - Options for the third digit: 10 So, the total number of area codes is: \[ 8 \times 10 \times 10 = 800 \] Next, let's calculate how many 10-digit phone numbers are possible. The structure of a telephone number in the US and Canada typically follows the format NPA-NXX-XXXX, where: - NPA is the area code (3 digits) - NXX is the exchange number (3 digits) - XXXX is the subscriber number (4 digits), which can be any digit from 0 to 9. Since we already calculated the number of valid area codes as 800, and exchange numbers also follow the same rules as area codes (2-9 for the first digit and 0-9 for the next two): - Total exchange codes: \( 8 \times 10 \times 10 = 800 \) - The subscriber number (XXXX) can be any combination of 4 digits (0-9), giving \( 10 \times 10 \times 10 \times 10 = 10,000 \) possibilities. Now, we can multiply these together for the total number of 10-digit phone numbers: \[ 800 \text{ (area codes)} \times 800 \text{ (exchange numbers)} \times 10,000 \text{ (subscriber numbers)} = 6,400,000,000 \] Thus, the total number of 10-digit phone numbers possible under these rules is **6,400,000,000**.