Chapter 16.2, Problem 8P

A pizza parlor problem. How many different large pizzas with no double toppings can be made? (For example, mushroom, pepperoni, and sausage is one possibility, and so is mushroom and sausage, but not double mushroom and sausage. Your count should also include the case of no toppings.) You can’t answer the question yet because you don’t know how many toppings the pizza parlor offers.
a. Determine the number of different pizzas when there are exactly 3 toppings to choose from (e.g., mushroom, pepperoni, and sausage).
b. Determine the number of different pizzas when there are exactly 4 toppings to choose from.
c. Determine the number of different pizzas when there are exactly 5 toppings to choose from.
d. Look for a pattern in your answers in parts (a), (b), and (c). Based on the pattern you see, predict the number of different pizzas when there are lo toppings to choose from.
e. Now find a different way to determine the number ofdifferent pizzas when there are lo toppings to choosefrom. This time, think about the situation in the followingway: Pepperoni can be either on or off, mushrooms canbe either on or off, sausage can be either on or off, andso on, for all 10 toppings. Explain clearly how to use thisidea to answer the question and why this method is valid.