We want to find the number of different subsets (of any size) in a [[Sample Space]]. When we view this as a [[Basic Counting Principal|tree diagram]], each element forms a stage that has 2 options (”in” or “out” of a subset). In a sample space of $n$ elements, there are $n$ stages where each $r_i=2.$ $ \prod_{i=1}^n r_i = \prod_{i=1}^n 2 =2^n $ ![[number-of-subsets.png|center|400]] **Note:** With this approach also the empty set $\emptyset$ and the full sample space $\Omega$ are considered as possible subsets.