Suppose there are $62$ characters available for a password ($26$ uppercase letters, $26$ lowercase letters, and 10 numerals).
How many passwords are there that are exactly $12$ characters long if the passwords contain the same number of uppercase, lowercase, and numeral characters (without repetition)?
Why wouldn't the answer just be:
$(26×25×24×23)^2 + (10×9×8×7)$
Here's another: The password must be between 10 and 12 characters and may contain repetitions aside from the ith character being the same as the (i-1)th character or (i+1)th character. That is, the password cannot have immediate repetitions.