Problem number 18. Six people each order one scoop of ice cream. They order three scoops of vanilla, two scoops of chocolate, and one scoop of lemon. They top the ice cream with three cherries, two wafers, and one chocolate chip. They use one topping on each scoop and no two ice cream desserts are the same. Which of the following combinations is not possible? A. Chocolate over cherry. B. vanilla over cherry. C. Lemon over wafer. D. Chocolate over wafer. E. Vanilla over chocolate chip. The picture will help us figure out where to distribute the various toppings. We have three scoops of vanilla, two scoops of chocolate, and one scoop of lemon. We have three different types of toppings. In order to make each of the vanilla cones look different, we're going to put a different topping on each one. So one of them will have a cherry, one will have a wafer, and one will get the one chocolate chip. So we've used up one cherry, one wafer, and the chocolate. We only have two types of toppings left now. Cherries and a wafer. So to make the two chocolate cones look different, one will get a cherry and one will get the wafer. So we've used those up and we're only left with one cherry that will go on the lemon. Let's compare the answers to what we got for our arrangements. A. Chocolate over cherry. We have that one, so this is not an answer that's impossible. Vanilla over cherry is also possible. In fact, the vanilla cones get one each of every topping. Lemon over wafer, well this was our lemon cone and we had put a cherry on it, so this one did not happen. Chocolate over wafer, we have a chocolate over wafer, and vanilla over chocolate chip. Yes, the chocolate chip went on the vanilla. So the one that is not possible of the ones listed is C. Lemon over wafer. So C is the answer.

ice cream

toppings

vanilla

chocolate

lemon