Question

At a pizza Parlour, you can order single, double, triple cheese in the crust. You also have the option to include ham, olives, pepperoni, bell pepper, meat ball, tomato slices and pineapple. how many different types of pizza are available at the pizza Parlour?

Answer 1

381 different types of pizza (assuming you can choose from 1 to 7 ingredients)

Explanation:

We are going to assume that you can order your pizza with 1 to 7 ingredients.

• If you want to choose 1 ingredient out of 7 you have 7 ways to do so.

• If you want to choose 2 ingredients out of 7 you have C₇,₂= 21 ways to do so

• If you want to choose 3 ingredients out of 7 you have C₇,₃= 35 ways to do so

• If you want to choose 4 ingredients out of 7 you have C₇,₄= 35 ways to do so

• If you want to choose 5 ingredients out of 7 you have C₇,₅= 21 ways to do so

• If you want to choose 6 ingredients out of 7 you have C₇,₆= 7 ways to do so

• If you want to choose 7 ingredients out of 7 you have C₇,₇= 1 ways to do so

So, in total you have 7 + 21 + 35 + 35 + 21 +7 + 1 = 127 ways of selecting ingredients.

But then you have 3 different options to order cheese, so you can combine each one of these 127 ways of selecting ingredients with a single, double or triple cheese in the crust.

Therefore you have 127 x 3 = 381 ways of combining your ingredients with the cheese crust.

Therefore, there are 381 different types of pizza.