Question

Mario's Pizza has 2 choices of crust: deep dish and thin-and-crispy. The restaurant also has a choice of 5 toppings: tomatoes, sausage, peppers, onions, and pepperoni. Finally, Mario's offers every pizza in extra cheese as well as regular. If Linda's volleyball team decides to order a pizza with 4 toppings, how many different choices do the teammates have at Mario's Pizza?

• A. $24$
• B. $32$
• C. $28$
• D. $20$

Answer 1

Answer: (D)

$20$

20 choices: Consider the toppings first. Model the toppings with the "word" YYYYN, in which four of the toppings are on the pizza and one is not. The number of anagrams for this "word" is:

$\frac{5!}{4!}=5$

If each of these pizzas can also be offered in 2 choices of crust, there are $5\times 2=10$ pizzas. The same logic applies for extra cheese and regular: $10\times 2=20.$