the question is in the description part.

Question

Question: 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, a digit, or one of six special characters *,>,<,!,+ and =.

 

 

A). How many different passwords are available for this computer?

 

B). How many ways of there passwords contain at least one occurrence of at least one of the special characters?

 

C). If it makes one nanosecond for a hacker to check whether each possible password is your password, how long would it take this hacker to try every possible password

Answer 1

We know that eight of the characters have 26+10+6=42 possible values ( letters, numbers or special characters) and the other four have 43 (they could not exist). 

So there are 43^4*42^8 possible passwords.

 

There are 26+10=36^8*37^4 possible passwords without special characters. So subtract this from part a) for those with at least one special character.

 

Divide the answer from part a) by 10^9 for number of seconds to guess your password.

 

Hope That helps,

Deanna