Quant combinations question confusion

GRE Quant Problem Solving
1

Hi GregMat Forum, I need some help understanding why my answer to this question was incorrect: A certain ice-cream shop has 40 toppings to choose from. If a customer can choose any combination of toppings, or none at all, how many different topping combinations exist?

I put 40!, because I was thinking of each option as a different cup combination: cup #1 would have all 40 toppings, cup #2 would have 39 toppings, etc. I thought this would result in how many different topping combinations could exist.

Why is this incorrect?

I’ve watched the PrepSwift video and I understand why 2^40 is correct, how each option is a binary choice of yes/no to the topping, and you could do this 40 times for the 40 toppings. I just want to better understand why 40! is wrong. Thank you!

2
  • You are implicitly assuming that all 40 toppings are going to be added
  • As a result, what you’re doing is basically rearranging these 40 toppings, which doesn’t matter in an ice-cream.