Question 6: Lectures 3 and 4. The Carleton Computer Science Society is having a plzza night, so you go to pick up some pizzas at Pizza Nerd{] Pizza Nerds has the following 8 toppings: pepperoni, sausage, ham, mushrooms, peppers, onions, olives, bacon. Each plzza vou order will have 4 toppings. However, knowing that computer scientists hate vegetables, each pizza you order should have at most one vegetable, that is, at most one of the following toppings: peppers, onions, or olives (it can also have none of these vegetables). a) Count the number of different pizzas using the sum rule. b) Count the number of different pizzas using the complement rule. ) Use the two answer above to show that () = () +3-(3) +3- () + (})- d) If vou allowed any combination of toppings (including no toppings, i.e.. just cheese and sauce), how many different pizzas could you make