Q1. Prove the following statement by induction.

For all non-negative integers n greater than 3 ( n>3), prove n! > 2n, state the mathematical induction and show work clearly.

Q2. Student are required to create 6-character long password to access the library. The letters must be from lowercase or digits. Each password must start with "a" or "b", it also must contain at most three lowercase letters( including the the first letter) and contain no repeated digits (letters can be repeated). How many valid passwords are there?, Show step by step working.