Suppose that a class of 20 students is assigned to write an essay. Suppose 3 essays are picked at random. How many groups of 3 are possible? What if the 3 essays picked at random are given awards of $20, $10, and $5. How many groups of 3 are possible now?

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?