Eight character passwords

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 of each of the three types is used?

First how many total 8 character passwords are possible? $\displaystyle 62^8$

Second how many 8 character passwords without any digits are possible? $\displaystyle 52^8$

Third how many 8 character passwords without any lowercase letters are possible? $\displaystyle 36^8$

Finally how many 8 character passwords without any uppercase letters are possible? $\displaystyle 36^8$

The answer should be $\displaystyle 62^8$ - $\displaystyle 52^8$ - $\displaystyle 36^8$ - $\displaystyle 36^8$; correct?