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Counting problems (contest style)
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Learn it Count systematically so you don't miss or double-count. For handshakes: n people × (n − 1) ÷ 2. For choices: multiply the number of options.
Example: How many handshakes if 6 people each shake hands once with everyone else?
- Each person shakes 5 hands: $6 \times 5 = 30$.
- But each handshake involves 2 people, so it was counted twice.
- $30 \div 2 = 15$ handshakes.
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