Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 8 businessmen, how many possible team submissions are possible?\nOptions:\n(A) 76\n(B) 100\n(C) 164\n(D) 198\n(E) 202 Random thoughts:
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We have 3 scenarios here:\n1) 1 tech2 businessmen: 4C1 x 8C2 = 112\n2) 2 tech1 businessman: 4C2 x 8C1 = 48\n3) 3 tech0 businessmen: 4C3 = 4\nTotal: 112+48+4 = 164 The final answer: (C).
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