1. ## Permutations

An ice cream store offers 20 different topping combinations, each one composed of two different items. Determine how many actual topping there are.

So i'm not sure at all how to do this question but what i think is you have to divide the 20 by 2 getting 10 and then do 10nPr2 which equals 90. I know this is not right at all but i really am lost here.

The answer in the back of the book is 5
Would i just divided the 10 by 2 again? Why? I don't understand

2. Originally Posted by tmas
An ice cream store offers 20 different topping combinations, each one composed of two different items. Determine how many actual topping there are.
The answer in the back of the book is 5
I have either written or edited a thousand of these questions.
This is one of the poorest.

But the good news is that I can explain the suggested answer.
If we count peanuts and chocolate as a combination, then there are two ways to do that. More of one that the other, say one first then the other.
Now, I think that that is counter-intuitive.
But the key may be in the title: permutations
Using permutations is the only rational way to get 5 as an answer: $\displaystyle P(n,2)=20$ implies $\displaystyle n=5$.

Again, this a very poorly worded question.