Students are in a class. 16 are civil engineering (CE) majors, 7 are computer science majors (CS), 10 are business majors (B), 6 are math majors (M), 2 are English majors (E), and 4 are animal science majors (AS). If you randomly select 8 students from the class without replacement and without regard to order, give the number of ways the following events could occur. a) Exactly 4 of the students are CS majors

b) 2 E, 3 CE, 1 AS, 1 M, 1 CS

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?