1. **Problem:** How many handshakes occur if eight people each shake hands with every other person exactly once? 2. **Formula:** The number of handshakes among $n$ people is given by the combination formula for choosing 2 people out of $n$: $$\text{Handshakes} = \binom{n}{2} = \frac{n(n-1)}{2}$$ 3. **Explanation:** Each handshake involves 2 people, and each pair shakes hands once. So we count all unique pairs. 4. **Calculation:** For $n=8$, $$\text{Handshakes} = \frac{8 \times (8-1)}{2} = \frac{8 \times 7}{2} = \frac{56}{2} = 28$$ 5. **Answer:** There are 28 handshakes in total.