Which of the problems below is not a permutation?

a. the number of ways 20 people can finish in the first three places in a race.

b. how many different kinds of pizza can be made with 12 optional toppings

c. how many ways 15 people can arrange themselves in a straight line

d. how many way is the top 20 hit songs can be arranged my selection 500 current singles.

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?