Question 1152008
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Here is a more sophisticated method for counting the number of handshakes; it is especially useful when the number of people is large.<br>
Suppose the number of people is n.  Then each of the n people shakes hands with each of the other (n-1) people, making a total of n*(n-1) handshakes.<br>
But when you count all of the handshakes by all the people in that way, you count each distinct handshake twice; so the actual number of handshakes is (n*(n-1))/2.<br>
In this problem, with 5 people, that gives you (5*(5-1))/2 = (5*4)/2 = 10.<br>
Of course, adding 4+3+2+1 is faster than that.... But if the number of people were 79 instead of 4, you wouldn't want to be adding 78+77+76+...+3+2+1 to find the number of handshakes.<br>