How many $4$-digit numbers of the form $\overline{1a2b}$ are divisible by $3?$
Hello I am new here so I don’t really know how this works. I know that for something to be divisible by 3, you add the digits and see if they are divisible by $3$. So that means $3+a+b=6, 9, 12, 15, 18,$ or $21.$ I’m just confused about how to calculate the number of cases.