How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero)?
a. 567,000,000
b. 486,000,000
c. 1,053,000,000
d. 729,000,000
e. 810,000,000
Thank you for helping.
9*10^3 * 9*10^4
Ah, numbers! Let's crunch some digits together, shall we? To figure out the number of international direct-dialing numbers, we need to consider two things: the area code and the telephone number.
For the area code, we have four digits to work with, with the first digit being non-zero. This means we have 9 options for the first digit (1 to 9) and 10 options for each of the remaining three digits (0 to 9). That gives us a total of: 9 * 10 * 10 * 10 = 9,000 possibilities for the area code.
Now, for the telephone number, we have five digits to play with, again with the first digit being non-zero. So, we have 9 options for the first digit and 10 options for each of the remaining four digits. This gives us: 9 * 10 * 10 * 10 * 10 = 90,000 possibilities for the telephone number.
To calculate the total number of international direct-dialing numbers, we simply multiply the possibilities for the area code by the possibilities for the telephone number: 9,000 * 90,000 = 810,000,000.
So, the answer is e. 810,000,000. That's a whole lot of numbers to dial! Happy calling!
To find the number of possible international direct-dialing numbers, we need to calculate the number of options for each part of the number (area code and telephone number) and then multiply them together.
For the area code:
- The first digit must be nonzero, so there are 9 options (1-9).
- The remaining three digits can be any number from 0-9, so each digit has 10 options.
- So, the total number of options for the area code is 9 * 10 * 10 * 10 = 9,000.
For the telephone number:
- Like the area code, the first digit must be nonzero, so there are 9 options (1-9).
- The remaining four digits can also be any number from 0-9, so each digit has 10 options.
- So, the total number of options for the telephone number is 9 * 10 * 10 * 10 * 10 = 90,000.
Finally, to find the total number of possible combinations, we multiply the options for the area code and the telephone number:
9,000 * 90,000 = 810,000,000
Therefore, the correct answer is (e) 810,000,000.
To find the number of international direct-dialing numbers possible, we need to consider the options available for both the area code and the telephone number.
For the area code, the first digit must be nonzero. This means that we have 9 options (1 to 9) for the first digit. For the remaining three digits, we have 10 options (0 to 9). Therefore, the total number of possibilities for the area code is 9 * 10 * 10 * 10 = 9,000.
For the telephone number, similarly, the first digit must be nonzero. So, we also have 9 options for the first digit. For the remaining four digits, we have 10 options. Therefore, the total number of possibilities for the telephone number is 9 * 10 * 10 * 10 * 10 = 90,000.
Now, to find the total number of international direct-dialing numbers possible, we multiply the number of possibilities for the area code with the number of possibilities for the telephone number. So, the total number of possibilities is 9,000 * 90,000 = 810,000,000.
Therefore, the answer is e. 810,000,000.