Question 1 (14 points) Use mathematical induction to prove that for any positive integer n, 6 evenly divides 7" - 1. Note: 6 evenly divides an integer num, if and only if num is a multiple of 6. For example, 6 evenly divides 18 (18 is a multiple of 6). Question 2 (12 points) You are creating a 4-digit pin code. How many choices are there where exactly one digit appears more than once? Explain your answer. Question 3 (15 points) Two fair dice are rolled. Let X be the random variable: if the values in the dice are d, and d2, then X = max (d1. dz) For example: . if when rolling the dice, you get 4 and 3, X would be 4 . If when rolling the dice, you get 2 and 2, X would be 2. a. Find the distribution of X. That is, for each possible value of X, say what is the probability X would get that value. b. What is E(X)? That is, find the expected value of X. Explain your answers