Counting number of license plates How many license plates can be made using 4 digits followed by 3 letters or 4 letters followed by 3 digits?

My attempt is the following. First, there are $9^4 \times 26^3$ license plates using 4 digits followed by 3 letters. Second, there are $26^4 \times 9^3$ license plates using 4 letters followed by 3 digits. Thus, in total there are:

$$9^4 \times 26^3 + 26^4 \times 9^3$$

possible combinations. Is this correct?
Since there are 10 digits (0-9) and 26 letters (a-z), the total number of valid combinations equals:

$$10^4 \cdot 26^3 + 26^4 \cdot 10^3 = 458,803,904$$
I suppose there is a slight error
The first digit is not zero hence 9 ways but for the rest there should be 10 ways
Hence correct answer will be
9×10^3×26^3+26^4+9×10^2