Question

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

Answer 1

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

Explanation:

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.