Suppose you're given a task to find the number of configurations for a password with the following stipulations;
1) there must be at least 8 characters (and let's assume a limit of 16 characters)
2) there must be at least 1 upper case character and at least 1 lower case
3) there must be at least 1 digit
4) there must be at least 1 special character (e.g., ., -, _, !, @, *, %)
With 26 letters both lower case and upper case (a-z), 10 digits (0-9), and 33 special characters, it seems we have a total combination of $95^8$ (of course, this is too simple because we don't want to neglect or re-use any of the above stipulations).
In the end, how many configurations may exist in an orderless, ≥8-character password such as this? Can you demonstrate how this is solved using summation notation?