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)?
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