Finite Math

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)?

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  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

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