Phone numbers consist of a three-digit area code followed by seven digits. if the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, how many different phone numbers are possible? how did you come up with your answer?

Let's start with the three digit area code first.
We have three slots to fill.

The first slot cannot start with 0 or 1, which leaves us 2, 3, 4 ..., 9 to fill.
This means we have 8 different arrangements for the first slot.

The second slot MUST have a 0 or 1 for the second digit, which leaves us with 2 different arrangements.

There are no restrictions for the third slot, so we would have 10 different arrangements.

Thus, the total arrangement of area code is 8 · 2 · 10 = 160 different arrangements.

Now, let's explore the total arrangements of telephone numbers.
There is only one restriction, and that's on the first number.

Thus, the total number of ways is:
8 · 10 · 10 · 10 · 10 · 10 · 10 = 8, 000, 000

Since we want them simultaneously, we want to multiply the two arrangements to find the total number of arrangements.

Total arrangements: 160 · 8, 000, 000 = 1 280 000 000 different ways.

The answer simplified would be. -6300x

0.03030303030 or