If set S has n elements, then C(n,k) is the number of ways of choosing k elements from S.

Thus, the number of subsets of S of all possible values is given by,

C(n,0) + C(n,1) + C(n,2) + . . . . . . . . . . + C(n,n) = 2ⁿ

Comparing the given equation with the above equation we get,

2ⁿ = 256

2ⁿ = 2⁸

n = 8

²ⁿC₂ = ¹⁶C₂

= 120