Question 2: See Lecture 2. You are going to pub night at your local pub (where you happen to see your instructor doing "research"). This pub has the following selection of drinks: 5 different types of craft beer, B1, B2, B3, B4, B5, 4 different types of cider, C1, C2, C3, C4, and 3 different types of soda, S1, S2, S3. Over the course of the evening you have 5 drinks. In each of the following scenarios, count the number of possible drink combinations (the order of the drinks matters): a) You have 5 drinks of any type and drinks may be repeated. b) You have 5 drinks of any type, but do not have the same drink twice in a row. c) You have 5 drinks, but limit yourself to exactly 1 beer and exactly 1 cider. d) You have 5 drinks and at least 1 of the drinks is a soda. e) You have 5 drinks, and you have at least 1 soda, at least 1 beer, and at least 1 cider. f) You have at most 3 beer and you have 0 cider. g) You have at least 4 beer and you have 0 cider. h) Use your answers to f) and g) above to prove that 0 (5135-1 = 85. Question 3: Lecture 5: Pascal's Triangle You are at the same place as in the previous question, with the same selection of drinks, but now you want to get 8 drinks to go. What this means is that the order of the drinks no longer matters we only care about how many of each drink you have. a) How many ways total can you order 8 drinks? Remember, order doesn't matter. b) How many ways can you order 3 beer, 2 cider, and 3 sodas? c) How many ways can you order 8 drinks if you order at least 2 of B and at least 1 of C?