How many subsets of S have at most 2 elements?

Question

Assume that the set S has 11 elements.
How many subsets of S have at most 2 elements?

Answer 1

Set S has 11 elements

all the subsets that have at most 2 elements means all the subsets with 2 elements, all the subsets with only 1 element and the empty set or null set

how many ways can you choose 2 elements from 11 elements ?

11!/2!(11-2)!

11!/2!9!

11*10/2=110/2=55 subsets with exactly 2 elements

11 subsets with only 1 element

and the null set or empty set, Ø

55+11+1=67 subsets with at most 2 elements