Let X1, X2, X3, X4, X5, and X6 denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these Xis have a multinomial distribution. According to the M&M web site, the color proportions are p1
.24, p2
.13, p3
.16, p4

.20, p5
.13, and p6
.14.

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?