In a meeting of 3 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 answers
A) 125  B) 120  C) 110  D) 90  E) 100
In fact, all 15 people will shake hands with 12 others.   So, it SEEMS like the TOTAL number of handshakes = (15)(12)   HOWEVER, we need to keep in mind that we have counted each handshake TWICE.   To account for this DUPLICATION, we must divide (15)(12) by 2.   So, the TOTAL # of handshakes = (15)(12)/2 = 90   Answer : 90
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In a meeting of 3 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?