Permutation

[Guest]

Consider 10-character alphanumeric passwords (that is, made up of letters of the English alphabet, either lowercase or uppercase, and decimal digits). How many such that contain at least one lowercase letter, at least one uppercase letter, at least one digit, but do not contain your birthday in the format ddmmyyyy.
(E.g. my birthday is 06091978 so should not count the password A06091978x.)