A pizza parlor offers whole-wheat, white, and gluten-free crust options. The who

Question

A pizza parlor offers whole-wheat, white, and gluten-free crust options. The whole-wheat crust comes in three sizes, the white crust comes in four sizes and the gluten-free comes in two sizes.

a. how many crust options does the parlor offer.
b. Any pizza can be topped with exactly one of the following cheeses: full-fat mozzerella, reduced-fat mozzerella or soy cheese. How many choices does a customer have for plain cheese pizza.
c. Suppose that the pizza parlor offers 5 meat toppings and 7 vegetable toppings. How many ways can the customer choose a pizza with 3 distinct toppings? ( remember to factor in the choice of crust and cheese).
d. How many ways can a customer choose vegetarian pizza with 3 distinct toppings? Remember to factor in the choices of crust and cheese).

Explanation / Answer

a: There are 3 whole wheat + 4 white + 2 gluten-free crusts, for a total of 9 different crusts. b: There are 3 different cheese options that can be ordered with any of the 9 crust options, so there are 9 * 3 = 27 different ways to order a plain cheese pizza. c: There are 5 meat + 7 veg toppings, so there are 12 choose 3 = 12!/(9!3!) = 220 different three distinct topping combinations for each of the 27 different crust and cheese options, for a total of 27 * 220 = 5940 possibilities. d: The three vegetarian topping pizzas would be counted like the previous except using 7 instead of 12 for the number of toppings. 7 choose 3 = 7!/(4!3!) = 35; 27 * 35 = 945 different vegetarian pizzas with three distinct toppings.

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