Permutations and combinat

Question

Computer password with 8 characters, but no more than 12 characters, where each character in the password is a lowercase, an uppercase letter, a digit, or one of the 6 special character. How many different passwords are available for this computer system?

Answer 1

You Character set has a size of $$|\Omega| = 26_{\text{upper}} + 26_{\text{lower}} + 10_{\text{digit}} + 6_{\text{symbol}} = 68$$ So the total amount is $$A = \sum_{n=8}^{12} 68^n$$ Evaluation of $A$ is up to you.