Final answer:
In a group of five people where everyone shakes hands with each other once, there are a total of 10 possible handshakes. This is calculated using the combinatorial formula n(n - 1) / 2.
Step-by-step explanation:
The problem of determining how many handshakes occur if everyone in a group of five shakes hands exactly once with every other person is a classic problem in combinatorics, which is a branch of mathematics. The formula to find the number of handshakes is n(n - 1) / 2, where n is the number of people. This formula prevents counting any handshake more than once.
For our case with five people the calculation will be:
5(5 - 1) / 2 = 5(4) / 2 = 20 / 2 = 10
Therefore, there are 10 possible handshakes.