The number of subsets of S containing k elements is equal to (nk)=k!(n−k)!n!, where n=∣S∣=200.
Firstly, find the number m of subsets of S containing not more than 2 elements. The emptyset is a unique set containg no elements. There are 200 different subsets of S having one element. The number of subsets containg two elements is (2002)=2!⋅198!200!=2⋅198!200⋅199⋅198!=100⋅199=19900.
Then m=1+200+19900=20101. Since the set S contains 2200 subsets, the number of subsets of S containing more than 2 elements is 2200−m=2200−20101.
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