Question

In the Metro Atlanta area, how many phone numbers are possible using the area code 404? The restrictions for the phone company are listed below.

- The first digit of the phone number cannot be numbers 0-4.
- The second number cannot be a zero.
- The third and fourth numbers cannot be a zero or one
- The fifth number cannot be a zero, one or two .
a. 3000 phone numbers
b. 2016000 phone numbers
c. 30 phone numbers
d. 20160 phone numbers

Answer 1

Option D). The total number of phone numbers possible using the area code 404 in the Metro Atlanta area is 20160.

Step-by-step explanation:

In the Metro Atlanta area, the number of possible phone numbers using the area code 404 can be calculated by considering the restrictions set by the phone company. The restrictions are as follows:

1. The first digit of the phone number cannot be numbers 0-4.
2. The second number cannot be zero.
3. The third and fourth numbers cannot be zero or one.
4. The fifth number cannot be zero, one, or two.

To calculate the total number of phone numbers, we need to find the number of possibilities for each digit and multiply them together.

For the first digit, there are 5 possibilities (5, 6, 7, 8, and 9).

For the second digit, there are 9 possibilities (1, 2, 3, 4, 5, 6, 7, 8, and 9).

For the third and fourth digits, there are 8 possibilities for each digit (3, 4, 5, 6, 7, 8, and 9).

For the fifth digit, there are 7 possibilities (3, 4, 5, 6, 7, 8, and 9).

Therefore, the total number of possible phone numbers is calculated as: 5 x 9 x 8 x 8 x 7 = 20,160 phone numbers.