Question 840535
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Hi,
Suppose there are 6 people in a room. Each of those 6 would shake hands with 5 others. 
Thus, we have 6 * 5. However, there would be handshakes between each pair twice. 
we must divide by two, giving us the formula: 
6*5/2 or, generalized to n(n-1)/2.

___1___2___3__4__5__6
1|1,1 1,2  1,3 etc
2|2,1 etc
3|3,1 _etc
4|
5|