[INST] 23 people attend a party. Each person shakes hands with at most 22 other people. What is the maximum possible number of handshakes, assuming that any two people can shake hands at most once?/n [/INST]  ###Response: Note that if each person shakes hands with every other person, then the number of handshakes is maximized. There are C(23,2) = (23)(22)/2 = (23)(11) = 230+23 = 253 ways to choose two people to form a handshake.