Answer
$2^{100}$ - 5051 subsets with more than two elements.
Work Step by Step
Number of subsets with more than 2 elements = Total subsets - Subsets with at most 2 elements.
Total subsets = $2^{100}$
Subsets with most 2 elements = $C$(100,2) + $C$(100,1) + $C$(100,0) = 4950 + 100 + 1 = 5051
Subsets with more than two elements = $2^{100}$ - 5051