Let X, X, X, X, X, and X denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these X's have a multinomial distribution. According to the M&M Web site, the color proportions are p = .24, p = .13, p = .16, .20, ps .13, and p = .14. P4

a. If n = 12, what is the probability that there are exactly two M&Ms of each color?

b. For n = 20, what is the probability that there are at most five orange candies? [Hint: Think of an orange candy as a success and any other color as a failure.]

c. In a sample of 20 M&Ms, what is the probability that the number of candies that are blue, green, or orange is at least 10?