A pizza restaurant offers four different sizes of pizza (personal, medium, large

Question

A pizza restaurant offers four different sizes of pizza (personal, medium, large, or party), three different types of crust (regular, deep dish, or thin), and can be ordered plain (no toppings) or may have 1 or more of the following toppings: (1) extra cheese, (2) pepperoni, (3) sausage, (4) beef, (5) Canadian bacon, (6) bbq chicken, (7) anchovies, (8) pineapple, (9) mushrooms, (10) green pepper, (11) black olives, (12) peperoncini, (13) artichokes, (14) tomato, (15) jalapeno, (16) onions, (17) feta cheese, and (18) ham. How many different pizzas does the restaurant offer? [Examples: A medium deep dish pizza with sausage, Canadian bacon, and black olives is one possible pizza. A personal pizza with thin crust and no toppings is another possibility. A regular crust party pizza with extra cheese is yet another choice.]

The answer is apparently 3.1Million. Any tips? My idea is to do 4 * 3 * 18!, but that gives the wrong answer. Any help is appreciated. Also, i see someone else asked this question in the past and was given a wrong answer. Thanks

Explanation / Answer

No toppings no. of pizza = 4* 3 = 12

With toppings:

We can have 1 topping, 2 toppings.....upto 18 toppoings in one pizza

So,

Number = 4 * 3 * (18C1 + 18C2.......+ 18C18)

N = 12 * (2* {18 + 153 + 816 + 3060 + 8568 + 18564 + 31824 + 43758} + 48620 + 1)

N = 3145728

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