Students are required to create 6-character long passwords to access the library. The letters must be from lowercase letters or digits. Each password must contain at least two lowercase-letters, at

least one digit and contains no repeated digits. How many valid passwords are there? You are required to show your work step-by-step. [9 marks] Note: 1hfgt1 is invalid because 1 appears more than once. 134ggg is valid because there are 3lower-case letters and digits are not repeated. 4. Consider the following automaton. a) Give an example of a string containing 11 that is accepted by the following automaton. [2 marks] b) Give an example of a string of length 8 that is rejected by the following automaton. [2 marks] C) Describe the language of this automaton in plain English. [4 marks] d) Describe the language of this automaton using Regular expression. [3 marks]