Permutations and Combinations problem

This one has really been troubling me. The question is:

**A computer program requires a password of at least 6 but no more than 8 characters. All letters (of the English alphabet, not case sensitive) and digits (0 to 9) may be used. The password must contain at least one digit and one letter. How many different passwords are possible?**

I used the indirect method for each case and got down to:

__Case 1__: 6 character password

36^6 - (26^6 + 10^6)

__Case 2__: 7 character password

36^7 - (26^7 + 10^7)

__Case 3__: 8 character password

36^8 - (26^8 + 10^8)

And then I added all the cases together. Is that correct?