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At a gathering of 10 people, each person must shake each other person's hand once. How many handshakes must there be?
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Well how many people involve an handshake?
Two.
Exactly.
Is order important?
It is 10C2, but why isn't it 2^10?
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Okay so you have the math right.
You assume that each people has a choice. The can shake hands or they can't shake hands.
They MUST shake hands. So you can't say 2^10 .
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