There are four people at a party. Each person shakes hands only once with every other person. How many handshakes occur?

Algebra foundations
asked 2020-10-25
There are four people at a party. Each person shakes hands only once with every other person. How many handshakes occur?

Answers (1)

The first person shakes hands with 3 people.
The second person shakes hands with 3 people as well, but we already counted his shake with the first person. The third person shakes hands with 3 people, but we already counted his shake with the first two people. We have already counted all of the shakes that the last person had because he shook hands with everyone else.
So the total number of handshakes was 3 + 2 + 1 = 6.

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