I am trying to understand this problem in GregMAT’s quant practice:

An ice cream shop has 1010 flavors of ice cream and customers are allowed to choose any combination of flavors, as long as at least one flavor is chosen and each flavor is chosen only once. If the order of the flavors does not matter, in how many ways can a customer create their ice cream?

The video solution suggests doing (2^10)-1. How come that answer can’t be solved by taking the sum of different combinations C(10,1) + C(10,2) + C(10,3) … + C(10,10)?