Just a little though exercise where the math is eluding me.

You have a pick a password of exactly eight characters. The universe of characters at your disposal are upper case letters (26), lower case letters (26), digits (10), and symbols (15 for this discussion). You must use at least one of each, so how many possible combinations are there?

I started with the total combinations (77^8) and then subtracted all combinations with just lowercase letters (26^8), all uppercase (26^8), just digits (10^8) and just symbols (15^8), but then I got stuck. The combinations that don’t contain at least one of each must be excluded so I have to get rid of, for example, combinations that don’t contain any letters or don’t contain any symbols, and then I thought there has to be an easier formula for this (one I knew once upon a time). Anyone want to take a shot?

Does this take into account that order matters? Because this seems like the formula for when order doesn’t matter.

For example, if I simplified and needed two characters from two pools or 3 and 4 choices respectively, I could say it’s 34 = 12, but that’s only in that order. To get all the choices I’d have to add 43 to come up with 24 possibilities. No?

Sure Eric. You have to choose exactly 8 characters as a password with the following rules:

1 from uppercase letters (26)
1 from lowercase letters (26)
1 from digits (10)
1 from symbols (15 for this discussion)

In total, there are 77 characters to choose from. So Lennox properly multiplied each group for the first four slots (262610*15) then multiplied that by 77^4 for the remaining 4 slots. Because order matters, that has to be multiplied by 8! for the total possibilities that fit those rules.