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? Choose the correct choice.
A) 76  B) 100  C) 164  D) 198  E) 202
We have 3 scenarios here:   1) 1 tech2 businessmen: 41641 x 81642 = 112   2) 2 tech1 businessman: 41642 x 81641 = 48   3) 3 tech0 businessmen: 41643 = 4   Total:  112+48+4= 
<gadget id="calculator"> 112+48+4</gadget>
<output>164</output>
164   Answer: 164
<result>C</result>
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?