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There will be 28 handshakes.

If you ask each person how many handshakes they had they will tell you 7 making 7 x 8 = 56 handshakes in all.

But every hand involves two people, so every handshake has been counted twice, thus there are 56 / 2 = 28 handshakes in all.

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Q: If there are 8 people at a party and every person shakes hands with everyone else at the party how many handshakes will there be?
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