The local ice cream shop in Dontrelle’s town is called 21 Choices. Why? Because they offer 21 different flavors of ice cream. Dontrelle likes all but three of the flavors that 21 Choices offers: bubble gum, butter pecan, and pistachio.   A 21 Choices “basic sundae” comes in three sizes—small, medium, or large—and includes one flavor of ice cream and one of 12 toppings. Dontrelle has enough money for a small or medium basic sundae. How many different sundaes could Dontrelle order that include only flavors that he likes? Dontrelle could order a cone with three scoops of ice cream instead of a sundae. He prefers to have three different flavors (for variety) and he considers the order of the flavors on his cone to be important. How many three-scoop cones with three different flavors that Dontrelle likes are possible at 21 Choices? Give your answer as a number and using nPk notation.

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.