How many eight-character passwords are there if each character is either an uppercase letter A-Z, a lowercase letter a-z, or a digit 0-9, and where at least one character and at least one number are used?

Total number of passwords possible = $\displaystyle 62^8$

then $\displaystyle 10^8$ of these are all numbers and $\displaystyle 52^8$ are all letters.

So the answer would be $\displaystyle 62^8$ - $\displaystyle 10^8$ - $\displaystyle 52^8$.

Correct?