In a meeting of 3 representatives from each of 8 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 most appropriate option:
A) 242 B) 232 C) 212 D) 262 E) 252
In fact, all 24 people will shake hands with 21 others.   So, it SEEMS like the TOTAL number of handshakes = (24)(21)   HOWEVER, we need to keep in mind that we have counted each handshake TWICE.   To account for this DUPLICATION, we must divide (24)(21) by 2.   So, the TOTAL # of handshakes = (24)(21)/2 = 252   Answer : 252
<result>E</result>
In a meeting of 3 representatives from each of 8 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?