3. Three men and three women were nominated for THREE positions on the school board. Suppose the three male are named A, B, and C, and the female are named D, E, and F. Further, suppose that the following statements are true: • There should be at least one male and at least one female to be selected; • If A won a position, so did D; . If neither C nor F won a position, then E did not win a position; If A did not win a position, then both D and E won positions; • C cannot be the only male candidate to be selected; Either E or F (or both) would win a position. There is only one way to choose three candidates to satisfy all criteria above. Please find that way and justify it to be the only valid choice.

1. Suppose a senior is choosing classes and must select from a set of equal value classes needed for graduation There are 15 classes, all offered at different times. The student must take 5 classes to graduate. a. How many possible course schedules can the student choose? b. Suppose another student in the same major also chooses a schedule from the same 15 courses, also 5 courses, and chooses them independently of the first student (say each class is equally likely to be chosen). What is the probability that the two students choose the exact same schedule?

3. Eight different people want to interview for the Defense Against the Dark Arts professorship at Hogwarts: Severus Snape, Tom Riddle, Remus Lupin, Dolores Umbridge, Mad-Eye Moody, Quirinus Quirrell, Barty Crouch, and Gilderoy Lockhart. Albus Dumbledore needs to interview the candidates. How many possible orders are there in which Dumbledore can interview the candidates if all of the following conditions must be simultaneously true? Snape must be interviewed before Riddle, • Dolores Umbridge is interviewed last, • Crouch and Moody must be interviewed at the same time in a joint interview, AND Lupin and Lockhart are interviewed consecutively (although we do not know which of the two is interviewed first)

and 4. A department store surveyed 428 shoppers, and the following information was obtained: 214 shoppers made a purchase, and 299 were satisfied with the service they received. If 52 of those who made a purchase were not satisfied with the service, how many shoppers did the following? a. made a purchase and were satisfied with the service b. made a purchase or were satisfied with the service c. were satisfied with the service but did not make a purchase d. were not satisfied and did not make a purchase a. b. с. 8. A reg foll had an