Suppose that a password for a computer system must have at least $8,$ but no more than $12,$ characters, where each character in the password is a lowercase English letter, an uppercase English letter, a digit, or one of the six special characters and $=.$

a$)$ How many different passwords are available for this computer system?

b$)$ How many of these passwords contain at least one occurrence of at least one of the six special characters?

c$)$ Using your answer to part $($a$),$ determine how long it takes a hacker to try every possible password, assuming that it takes one nanosecond for a hacker to check each possible password.