The Basic idea
Yes, the concept you're looping around is "how many possible passwords exist under these rules?", which is formally called the "Password Space".
The formula to figure out how big the password space is for a given set of rules is quite simple:
(num_allowed_symbols) ^ (password_length)
16 character password consisting only of lower case English letters: there are 26 lowers, so:
26 ^ 16 = 4.4x10^22 possible passwords
8 character password consisting of English letters of both cases, numeric digits, and special characters: depends on how many special characters you allow, but lets say
26 lowers + 26 uppers + 10 digits + 16 specials = 78 characters, so
78 ^ 8 = 1.4x10^15 possible passwords
Unicode: let's say there's around 100,000 valid unicode characters. Then you only need a 5 or 3 character password (respectively) to match the password spaces of
lowers, uppers, digits, specials.
but before we get too excited over these numbers ...
Where it gets real
The number of possible passwords above is only really useful as a measure of security if every possible password is equally likely to be chosen. In my experience this is not true since
graycat123 is a far more common password than
ǨΞᾃЯ ҉ℒⵞ௵ޘ↡╤ if using the whole unicode space, but don't ask me how to type that on an Android keyboard!)
This very quickly gets into psychology and user-habits and we often see stats like this:
SplashData estimates almost 10% of people have used at least one of the 25 worst passwords on this year’s list, and nearly 3% of people have used the worst password, 123456.
That's why you see more and more websites giving "password strength meters" next to the Change Password box -- these are checking your password against common lists, looking for dictionary words, looking for keyboard patterns, etc. These meters are a far better measure of password strength than just the length because, well, people are bad at choosing passwords.
Far better to use a password manager and let a machine choose your password so that
h&9R#d3*ng is just as likely as
graycat123. If you want passwords that you can remember, then a good option is to come up with passwords using the diceware trick.