First of all, I'm not strong in math, but always interested in learning more. This is an "intellectual satisfaction" type of question, meaning knowing the answer won't really impact anything, but will afford me a certain satisfaction by quenching my curiosity. Maybe someone out there would be willing to help me work through how to compute the possible combinations of a password? The company I work for has a system that historically utilized passwords of 8 (and exactly 8, no more, no less) alphanumeric characters. The only rule was that the first character could not be numeric; otherwise, repeated characters were okay. The password is not case sensitive. So there are 26 possibilities for the first character, and positions 2 - 8 can be any of 36 possibilities. In my mind, then, the number of password possibilities is expressed as 26x36x36x36x36x36x36x36. The result is 2+ trillion; 2,037,468,266,496 to be exact. The rules were recently changed so that the 8-character password must now contain at least one alphabetic character and one numeric character, as well as one of three special characters (#,!,~). The special character must be used in positions 2 - 7 only, not in the first or last position. My gut told me the total number of password possibilities had been reduced, because though the overall character base was increased from 36 to 39, two (the first and last) are still base 36, at least one of the characters is base 26, at least one is base 10, and at least one is only base 3. Maybe my gut was wrong though, because of the "at least" part of the scenario. Do the new rules have any mathematical limiting impact on the possibilities for the middle six characters? Is 36x39x39x39x39x39x39x36 = 4,560,291,914,256 the right answer? I have a feeling I'm overlooking something, and I'd appreciate someone giving me some clarity on this. Thanks!