A Starburst candy package has 12 pieces three each of four f

A Starburst candy package has 12 pieces, three each of four flavors: berry, lemon, orange and cherry. The pieces are arranged randomly in the pack. You draw the first four from the pack. (a) What is the probability that all four are the same flavor? (b) What is the probability that they are all different flavors? (c) What is the probability that your four pieces have exactly two each of two flavors?

Solution

There are 20C4 = 4845 ways to get 4 candies inside the bowl.

a)

This is impossible. There are only 3 of each flavor.

Thus, P(all 4 have the same flavor) = 0 [answer]

**********

b)

You can choose 3 ways for berry, lemon, orange, and cherry, respectively.

Thus, there are 3*3*3*3 = 81 ways to do that.

Thus, P(all different) = 81/4845 = 0.016718266 [answer]

********

c)

There are 4 flavors, so there are 4C2 = 6 ways to choose two flavors.

Also, for each flavor, there are 3C2 = 3 ways to choose.

Thus, the number of ways to do this is

(6 ways to choose 2 flavors)(3 ways to choose from flavor 1)(3 ways to choose from flavor 2)

= 54 ways

Thus,

P(exactly 2 of each of two flavors) = 54/4845 = 0.011145511 [answer]