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 cannot b 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 imme 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 few isla (Assume that the combined population is about \( 400,000,000 \).) How many possible area codes are there? 792 (Type a whole number.) How many 10-digit phone numbers are possible? Are there enough phone numbers for a combined population of \( 400,000,000 \) ? Select the correct choice (Type whole number.) A. There are enough phone numbers. There are a total of \( \square \) possible 10 -digit phone numbers, which is greater than \( 400,000,000 \). B. There are not enough phone numbers. There are a total of \( \square \) possible 10-digit phone numbers, which is less than \( 400,000,000 \).

To solve the problem, we will break it down into two parts: calculating the number of possible area codes and then calculating the total number of possible 10-digit phone numbers. ### Part 1: Calculating Area Codes 1. **First Digit**: 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. **Second and Third Digits**: The second and third digits can be any digit from \(0\) to \(9\). This gives us \(10\) options for each of these digits. 3. **Exclusion of 911**: We need to exclude the area code \(911\). Now, we can calculate the total number of area codes: \[ \text{Total Area Codes} = (\text{choices for first digit}) \times (\text{choices for second digit}) \times (\text{choices for third digit}) - 1 \] Substituting the values: \[ \text{Total Area Codes} = 8 \times 10 \times 10 - 1 \] Calculating this: \[ \text{Total Area Codes} = 800 - 1 = 799 \] ### Part 2: Calculating 10-Digit Phone Numbers 1. **Area Code**: We have already calculated \(799\) possible area codes. 2. **Exchange Numbers**: The exchange number also follows the same rules as the area code: - First digit: \(2-9\) (8 options) - Second and third digits: \(0-9\) (10 options each) Thus, the total number of exchange numbers is: \[ \text{Total Exchange Numbers} = 8 \times 10 \times 10 = 800 \] 3. **Line Numbers**: The line number can be any digit from \(0\) to \(9\) for each of the last four digits, giving us \(10\) options for each digit: \[ \text{Total Line Numbers} = 10 \times 10 \times 10 \times 10 = 10^4 = 10,000 \] Now, we can calculate the total number of 10-digit phone numbers: \[ \text{Total 10-Digit Phone Numbers} = (\text{Total Area Codes}) \times (\text{Total Exchange Numbers}) \times (\text{Total Line Numbers}) \] Substituting the values: \[ \text{Total 10-Digit Phone Numbers} = 799 \times 800 \times 10,000 \] Calculating this: \[ \text{Total 10-Digit Phone Numbers} = 799 \times 800 = 639200 \] \[ \text{Total 10-Digit Phone Numbers} = 639200 \times 10000 = 6392000000 \] ### Conclusion Now we can compare the total number of possible 10-digit phone numbers with the population of \(400,000,000\): - Total possible 10-digit phone numbers: \(6,392,000,000\) - Population: \(400,000,000\) Since \(6,392,000,000\) is greater than \(400,000,000\), we conclude: **A. There are enough phone numbers. There are a total of \(6,392,000,000\) possible 10-digit phone numbers, which is greater than \(400,000,000\).**