There are 4 representatives from each of 4 companies at a convention. At the start of the convention, every person shakes hands once with every person except the other representatives from their company. How many handshakes are there?
I want to count the number of handshakes that happen at the convention. I know that each person shakes hands with 12 other people, because they don't shake hands with the 3 people from their own company. So, each of the 16 people shakes hands 12 times. But, I don't want to double count the handshakes, because each handshake involves two people. So, I need to divide the total number of handshakes by 2 to get the number of unique handshakes. That means the number of handshakes is (16 * 12) / 2 = 96. 