Answer:
Choice B. 5,114,880 (There's a digit missing in the problem.)
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: any digit except 8 and 9.
Since you exclude 2 digits from the 10 possible digits, there are 8 choices left.
8 * _ * _ * _ * _ * _ * _
Second and third digits: any digit from 1 and 8.
Any digit from 1 to 8 means: 1, 2, 3, 4, 5, 6, 7, 8. That means there are 8 choices.
8 * 8 * 8 * _ * _ * _ * _
Last four digits: no restrictions (for now), so there are 10 choices for each digit. We will deal with the restriction of 4 equal digits below.
8 * 8 * 8 * 10 * 10 * 10 * 10
The product of the 7 numbers above is:
8 * 8 * 8 * 10 * 10 * 10 * 10 = 5,120,000
The last 4 digits cannot all be thee same. There are 10 ways they can all be the same: 0000, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999.
Each of the combinations of the first 3 digits cannot have 10 combinations of equal digits.
The number of combinations of the first 3 digits is: 8 * 8 * 8 = 512.
Each of these 512 combinations cannot have 10 combinations of equal digits for the last 4 digits. 512 * 10 = 5120.
We must subtract 5120 from 5,120,000 to find the final answer.
5,120,000 - 5120 = 5,114,880
. Combining like terms gives us the third degree polynomial we are looking for: 