how to solve this counting problem? Each user on a computer system has a password, which is six to eight characters long, where each character is an uppercase letter or a digit.  Each password must contain at least two digits. How many possible passwords are there?
Is the answer: $(36^6 - 26^5) + (36^7 - 26^6) + (36^8 - 26^7)$?

I would use
$$\left(36^6 - 26^6 - \binom{6}{1}\cdot 26^5\cdot 10 \right) + \left(36^7 - 26^7 - \binom{7}{1}\cdot 26^6\cdot 10 \right) + \left(36^8 - 26^8 - \binom{8}{1}\cdot 26^7\cdot 10 \right).$$
