At a local ice cream shop, you can choose from a collection of 11 different toppings. If you want to choose at least one topping, how many different topping combinations are possible (assuming no repeat toppings)?

Answer 1

number of subsets of 11 elements = 2^11 = 2048
This includes the null set, equivalent to having no topping.

Number of choices with at least one topping
= 2048-1 = 2047