The number of possible phone numbers in the 512 area code is 2,000,000
Here, we want to know the number of area codes possible.
To get this , we need to know the choices we have per number in the phone numbers set
For A , we have a restriction from 2-9
What this means is that, we are to select 1 out of eight choices.
The number of ways this can be done can be computed by the use of combination;
Hence, we have;
8 C 1 choices
For B , we have a restriction within 1-5
What this means is that we are to select 1 number within 1 to 5
The number of choices here will also be;
5 C 1 choices
For C , we have a restriction within 1-5
What this means is that we are to select 1 number within 1 to 5
The number of choices here will also be;
5 C 1 choices
For X, we have to choose from within 0 to 9
What this means is that we are to select one out of 10 choices;
The number of ways we can do this will be
10 C 1 choices
Kindly recall that we are to make a selection of X four times
What this means is that for the X region only we have (10 C 1 )^4 choices
Mathematically, for a number n;
n C 1 = n
So the number of possible phone numbers will be;
8 C 1 * 5 C 1 * 5 C 1 * (10 C 1)^4
Thus, we have
8 * 5 * 5 * 10 * 10 * 10^4 = 2,000,000