Q: Each user on a computer system has a password, which is six to eight characters long, where each character is an upper-case letter or a digit. Each password must contain at least one digit. How many possible passwords are there?
My approach : $6×36^5×10$ for password of length 6 and so on.
From this question on SO I get that some kind of over counting is happening here and I understand the solution in the book but just can't figure where my approach is wrong.