### Instruction: 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?### Response: 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.