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Question

Find an expression for the total number of handshakes needed if $n$ people all shake hands with each other.

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Answer 1 · 2018-05-22T21:41:17

$1+2+3+...+(n-1)$

Note that this explanation might be confusing.

Let's say three people shook hands with each other. Their names are A, B, C, and D.
A: B, C, D
B: A, C, D
C: A, B, D
D: A, B, C

Some are counted more than once. Cross them out.
A: B, C, D
B: C, D
C: D
D:
That is $1+2+3=6$ . Try this with other problems.