Counting passwords

Oct 2009
St. Louis Area
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 \(\displaystyle 62^8\) - \(\displaystyle 10^8\) - \(\displaystyle 52^8\).