Combination or Permutation, please help

[email protected] wrote: I have a book with a whole bunch of combo and perm examples and for instance here is a very simple one:

Theresa ordered a combo pizza with 3 different toppings. If there are 6 toppings to choose from and one of her toppings is mushrooms, how many different combo pizzas did she have to choose from?

I thought this was a combination problems and as there mushrooms are fixed it was a 5C3 so the answer is 10? Well its not the answer is 20? C

It's a pizza, so the order of the toppings doesn't matter (pineapple, mushrooms and bacon is the same pizza as bacon, mushrooms and pineapple). If we know we have mushrooms, we need to choose 2 toppings from the remaining 5, which we can do in 5C2 ways. Equivalently, we can choose 3 toppings to leave off of the pizza, which we can do in 5C3 ways. Either way, the answer should be 10, so either there's something else in the question (perhaps a choice of two different cheeses, which would double the answer?), or the book you're using has the wrong answer. Out of curiosity, what book is it? In any case, your interpretation is entirely correct.

beeparoo wrote:
Unless, the pizza has layers; like a bottom pepperoni layer, a middle mushroom layer, and top pineapple layer.

Brilliant- a layered pizza. A perfect illustration of when order should matter, and when it should not. Nice one!