Consider the following problem: A pizza parlor offers 5 different toppings for their pizzas: pepperoni, sausage, mushrooms, onions, and peppers. If a customer can choose up to 3 toppings, how many 3 topping pizzas can be ordered, if a customer may only choose each topping once? Does order matter in this situation? Is repetition allowed? What structure type best characterizes this problem? The answers to the following questions are the same: How many ordered lists of length 2 with entries taken from the set {0,1,2} are there? How many positive factors does 36 have? Select the factors of 36 that the following ordered lists corespond to: 0,0 0,2 1,2 (Hint: link each ordered list a,b to the positive factor 2a3b ) Consider a set of n distinct objects, and let S be the set of all possible permutations of these objects. Define a relation on S such that two permutations are equivalent if they differ by a transposition of adjacent objects. What is the size of the equivalence class of a given permutation