There are 12 participants at a meeting. Each person shakes hands with every other participant exactly once. How many handshakes occur?
Show hints
- First count 12 × 11 directed pairs.
- Divide 12 × 11 by 2 because each pair is repeated.
Show the answer and solution
Answer: 66
Each of the 12 participants is paired with 11 others, but every handshake is counted twice. Therefore, 12 × 11 ÷ 2 = 66.