you have a collection of 13 different toppings and you choose at least one. how many different combination are possible assuming no repeat toppings?

The power set of a set S is the set of all subsets of S. If S has n elements, there are 2^n elements in P(S).

That includes the empty set, which we cannot use (since we must have at least one topping).

So, there are 2^13 - 1 ways to choose some selection of toppings.