We count the total number of possibilities for the area codes in the next manner:
1. For the first digit of the codes, we have six options, these are; 3,4,5,6,7,8
2. For the second digit of the codes, three options\; 2,3,4
3. For the third digit of the codes with can put any digit number except 6,7 or 8, that restriction let us the following possibilities:0,1,2,3,4,5,9
We will use the multiplicative rule to count the total number of possible codes with this restrictions, that is we will apply a rule of the form:
[tex]total\text{ N' of codes=possibilities for the first digit}\times(possibilities\text{ for the second digid\rparen}\times(possibilities\text{ for the third digid\rparen}[/tex]In our the specific case
[tex]Total\text{ N' od codes=6}\times3\times7=126[/tex]Therefore, we conclude that with these restriction, the total number of codes is 126
