For the following, you can leave your answer as a sum or product of binomial coefficients and or permutation notation (P(n,k)) where appropriate. a) Suppose you're writing a Discrete Mathematics final and you have 22 questions in mind each covering a different topic. Due to time restrictions, you can only include 8 of these. How many different tests could you write? (assume order of the questions does not matter) b) Suppose you're taking a Discrete Mathematics final and there are 8 total questions. If you randomly pick a question to solve entirely before moving onto a new random question, how many different possible orders are there for you to solve the problems? Assume you have time to solve every problem. (For example, you may to do question 5 fırst, followed by question 2, then 7, 6, 1, 3, 8, and finally question 4). c) Suppose that 20 students take your discrete math final. The test is worth 150 points, so possible scores range from 0 to 150. After I've graded, how many ways are there for at least two students to have received the same score? (Hint: don't count this directly) d) Suppose that after all students take a Discrete Math final, they are given cookies. If I have 20 students and 40 cookies, how many ways are there to give at least one cookie to every student after they take the final exam?