Answer:
Choice C. 4,480,000
Step-by-step explanation:
You must see the number of choices you have for each digit. Then you multiply all those numbers of choices together.
There are 7 digits in the phone number, so you will be multiplying 7 numbers together.
_ * _ * _ * _ * _ * _ * _
First digit: between 3 and 9.
Mathematically speaking, a whole number between 3 and 9 is limited to 4, 5, 6, 7, 8. That means there are 5 choices.
5 * _ * _ * _ * _ * _ * _
Second and third digits: between 1 and 8.
Mathematically speaking, a whole number between 1 and 8 is limited to 2, 3, 4, 5, 6, 7. That means there are 6 choices.
5 * 6 * 6 * _ * _ * _ * _
Last four digits: no restrictions, so there are 10 choices for each digit.
5 * 6 * 6 * 10 * 10 * 10 * 10
The product of the 7 numbers above is:
5 * 6 * 6 * 10 * 10 * 10 * 10 = 1,800,000
Now we have a problem. The number 1,800,000 is not in the choices and neither is a close number.
The conclusion is that this is a poorly worded problem, and the word "between" is not being used correctly in a mathematical way.
Let's assume that by "any between 3 and 9", 3 and 9 are included. Also, between 1 and 8, 1 and 8 are included.
We can now change the solution to the following.
There are 7 digits in the phone number, so you will be multiplying 7 numbers together.
_ * _ * _ * _ * _ * _ * _
First digit: between 3 and 9.
Between 3 and 9 means here: 3, 4, 5, 6, 7, 8, 9. That means there are 7 choices.
7 * _ * _ * _ * _ * _ * _
Second and third digits: between 1 and 8.
Between 1 and 8 is means here 1, 2, 3, 4, 5, 6, 7, 8. That means there are 8 choices.
7 * 8 * 8 * _ * _ * _ * _
Last four digits: no restrictions, so there are 10 choices for each digit.
7 * 8 * 8 * 10 * 10 * 10 * 10
The product of the 7 numbers above is:
7 * 8 * 8 * 10 * 10 * 10 * 10 = 4,480,000
4,480,000 is choice C.
