Consider a set of desserts at a restaurant: (cheesecake, chocolate cake, pumpkin
ID: 3305141 • Letter: C
Question
Consider a set of desserts at a restaurant: (cheesecake, chocolate cake, pumpkin pie, blueberry pie, cherry pie) If you are allowed to choose a set of two desserts only, how many different sets of desserts are possible? The friend sitting next to you wants to try some of the dessert that you select and they are hoping to try the cheesecake, chocolate cake, and cherry pie. If the friend will be happy if they are able to try at least two of them, what is the probability that your friend will be happy? (Assume that the choices that you make are not influenced by their interests, meaning the events are independent) a. b.Explanation / Answer
a. There are 5 different desserts and we need to choose 2
This can be done in 5C2 = 10 ways.
b. Note that the number of subsets of a set with n elements = 2n
Total number of ways to select the desserts = 25 = 32.
If all of cheesecake, chocolate cake and cherry pie are selected, other selections can be done in 22 = 4 ways.
If two of cheesecake, chocolate cake and cherry pie are selected which can happen in 3C2 = 3 ways, the number of ways of selecting the other two = 22 = 4 ways. Overall number of selections = 3*4 = 12.
Thus we can choose atleast two of cheesecake, chocolate cake and cherry pie in 4 + 12 = 16 ways.
Probability = 16/32 = 1/2 or 0.5.