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jmc

prealgebra senior

Problem

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?
Solution
All 16 people shake hands with 12 other people (everyone except themselves and the other representatives from their company). In multiplying , each handshake is counted twice, so we divide by two to get the answer of handshakes.
Final answer
96