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17 people ( a1,a2------ a17) are invited to a party. The host & hostess shake hand with every invitee & also with each other. The invitee shake hands in a circular fashion i.e pairs ( a1,a2)(a2, a3)------(a16,a17)(a17,a1) shake hand and there are total 52 shake hands. Let S be the set such that every pair in S shake hands. Then at most size of the S is 4,1,2,3

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