[Math] Calculate number of password combinations

combinationscombinatorics

An eight-character password consisting of upper- and lowercase letters and at least one numeric digit (0–9):

My working:

Passwords including digits:
62^8

passwords with no digits:
52^8

Passwords with at least one digit:

(62^8)-(52^8) =
164 880 377 053 440.

Is this correct?
I was told it is wrong and the answer given was 62^8 = 2.1834011E+14

Best Answer

Number of password combinations =

total number of combinations formed from upper case, lower case and digits 0 to 9 - [number of combinations without any digit + number of combinations excluding either upper or lower case letters - number of combinations with only upper or only lower case letters] =

(62^8) - [52^8 + 2.36^8 - 2.26^8]