The Correct Answer and Explanation is:
Based on the partially legible text and standard telephone numbering conventions, the correct answer is 8,000,000.
Here is a detailed explanation:
The question asks for the total number of possible phone numbers that can be created within a specific area code, which appears to be 212. To determine this, we must understand the structure of a standard phone number in the North American Numbering Plan (NANP). A complete phone number consists of ten digits, formatted as a 3 digit area code, followed by a 7 digit local number. This 7 digit local number is further divided into a 3 digit central office code, also known as an exchange, and a 4 digit line number. The format is typically written as (NPA) NXX-XXXX.
In this problem, the area code (NPA) is already given as 212. This means the first three digits are fixed, and we only need to calculate the number of possible combinations for the remaining seven digits (NXX-XXXX).
Let’s first analyze the central office code, represented by NXX. There are specific rules governing which digits can be used in these positions. The first digit of the central office code, represented by ‘N’, historically could not be 0 or 1. These digits were reserved for special purposes, such as operator assistance (0) or indicating a long distance call (1). Therefore, the ‘N’ digit has 8 possible values: 2, 3, 4, 5, 6, 7, 8, or 9. The next two digits of the central office code, both represented by ‘X’, have no such restrictions. Each ‘X’ can be any digit from 0 through 9, giving them 10 possible values each. To find the total number of possible central office codes, we multiply the possibilities for each digit: 8 choices for ‘N’ × 10 choices for the first ‘X’ × 10 choices for the second ‘X’, which equals 800 possible central office codes.
Next, we consider the 4 digit line number, represented by XXXX. For these four positions, there are generally no restrictions. Each of the four digits can be any number from 0 to 9. This gives us 10 possibilities for each position. To calculate the total number of unique line numbers, we multiply the possibilities: 10 × 10 × 10 × 10, which equals 10,000 possible line numbers for each central office code.
To find the final answer, which is the total number of unique phone numbers within the 212 area code, we multiply the total number of possible central office codes by the total number of possible line numbers. This calculation is 800 (possible NXX codes) multiplied by 10,000 (possible XXXX line numbers), resulting in a total of 8,000,000. Therefore, there are eight million unique phone number combinations that can exist within the 212 area code.
