Sunday, August 21, 2005

How many pizza toppings are there, anyways?

Let's say you're running a pizza shop and you want to advertise how many different types of pizzas you can make. You have 10 different toppings to use, but of course you can combine them with others to make your pizza. How many pizzas can you make?

BTW, don't worry about people who want 'double' pepperoni.

1. The answer is 1024. Makes you wonder how they find all the space on the menu!

How to solve: If you have 10 toppings to choose from, then you can put on no toppings, one topping, two toppings, etc... So, we can count it like this:
For no toppings, that's easy, there's only one way to choose no toppings. For one topping, we have 10 toppings to choose from, so there are 10 ways of doing it. (BTW, we can use the same logic for 10 toppings and 9... There's only 1 way to put on 10 toppings, and only 10 ways to put on a combination of 9. But now it starts getting difficult. If we want to continue counting, we need the N choose K formula. Try doing a search!

2. 10C10+10C9+10C8...

Since order dosn't matter. I don't think many people think that mushrooms before pepperoni is diffrent from pepperoni before mushrooms. I guess if you have a Chicago style pizza...

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