MAT 121: Research Project 4

Possible Points:  100                                                                                                                           Points Earned:                      MAT 121: RESEARCH PROJECT 4 The purpose of this exercise is to explore applications of basic combinatorics and probability. Restaurant Menu Mayhem A new Italian restaurant named Pizza Possibilities has recently opened.  In order to try to carve their own place in a crowded restaurant market, they are offering some unusual options for their customers – “Choose Your Own Layers of Lasagna” and “Guess the Ingredients.” Layers of Lasagna – Many restaurants will allow their customers to choose from a list of ingredients in order to design a ‘custom’ lasagna dish, but only Pizza Possibilities allows the customer to choose the order in which the layers are stacked.  Pizza Possibilities offers the following list of ingredients that customers may choose from: Possible Lasagna Ingredients Meats Vegetables Cheeses Sauces Pasta Italian Sausage Tomatoes Ricotta Marinara Penne Bacon Onion Parmesan Alfredo Macaroni Ground Beef Green Pepper Mozzarella Pepperoni Zucchini There are several different types of lasagna the customer may order, based on the quantity and types of ingredients the customer prefers.   For each lasagna type, the customer may choose which ingredient will be used for each layer, with the only rules being that no ingredient may be chosen for more than one layer and that the bottom and top of the lasagna will consist of lasagna noodles (and thus do not need to be considered when determining how many options are possible for each lasagna type). For each of the types of lasagna, determine how many possible options there are for ordering that type of lasagna: Lasagna Types Possible Options Budget Lasagna (Choose 1 layer) Triple Layer Lasagna (Choose any 3 layers) Meat Lovers Lasagna (1st layer is your choice of Sauce, then choose any two Meat layers) Vegetarian Lasagna (1st layer is your choice of Sauce, then three more layers may be chosen from the Vegetables, Cheeses, and/or Pastas categories) Lucky Seven Lasagna (Choose any 7 layers) The Kitchen Sink Lasagna (Choose all 15 layers) Which type of lasagna provides the most options?  Which provides the least options? _________________________________________________________________ If Pizza Possibilities adds Chicken as a possible Lasagna ingredient, how many more possible options would there be for the Lucky Seven Lasagna? __________________________________________________________________ Pizza Probability – Pizza Possibilities also offers several types of pizza for their customers to choose from, in which the customers get to choose their toppings.  As a marketing gimmick, Pizza Possibilities will try to guess the combination of toppings chosen by the customer.  If Pizza Possibilities does not guess correctly, then the customer will get $1 off their order. Possible Pizza Toppings Pepperoni Chicken Tomatoes Pineapple Spinach Italian Sausage Ground Beef Onions Green Peppers Olives Bacon Ham Mushrooms Red Peppers Extra Cheese For each of the types of pizza, determine how many possible options there are for ordering that type of pizza (note that no topping may be chosen more than once): Pizza Types Possible Options Probability that Pizza Possibilities employee can guess your toppings correctly Snack Special Pizza (Choose any 1 topping) Triple Topping Pizza (Choose any 3 toppings) Meat Lovers Pizza (includes Extra Cheese and choice of any three meat toppings) Veggie-Style Pizza (Choose any 5 toppings that are not meats) Super Pizza (Choose any 8 toppings) Which type of pizza is the employee more likely to correctly guess the toppings for, the Triple Topping Pizza or the Meat Lovers Pizza? ___________________________________________________________________ What is the probability that the customer will get the $1 discount if they order the Super Pizza? ___________________________________________________________________ (Adapted from a project by 21st Century Math Projects https://1.cdn.edl.io/rUYs9csklVscHwF3CB8SJP5nlSOvBW0vhuSw3tSOcl2NyPEN.pdf ) Solved: GET ANSWER

Possible Points:  100                   ...