From a set of 4 items {a, b, c, d}, how many ways can you pick a subset (any size, including the empty set and the whole set)?
Subsets of an n-element set
2ⁿ
Each item is either in or out. Two choices, n times.
Try it
n = 4
2⁴ = 16 subsets. n = 10 gives 1,024. n = 20 gives over a million.
This is the same maths as binary digits. n switches with two states each = 2ⁿ outcomes.