In a meeting of 4 representatives from each of 5 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place? Choose the correct choice from the following options:
A) 170 B) 160 C) 180 D) 190 E) 200
In fact, all 20 people will shake hands with 16 others.   So, it SEEMS like the TOTAL number of handshakes = (20)(16)   HOWEVER, we need to keep in mind that we have counted each handshake TWICE.   To account for this DUPLICATION, we must divide (20)(16) by 2.   So, the TOTAL # of handshakes = (20)(16)/2 = 160   Answer : 160
<result>B</result>
In a meeting of 4 representatives from each of 5 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?