SOLUTION: At a party, 28 handshakes took place. Each person shook hands exactly once with each of the others present. How many people were at the party.?

Question 204427This question is from textbook
: At a party, 28 handshakes took place. Each person shook hands exactly once with each of the others present. How many people were at the party.? This question is from textbook

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
a couple of important thoughts ...
___ you don't shake hands with yourself
___ Bill shaking hands with Sue is the same as Sue shaking hands with Bill

so, N people shake hands with N-1 people ___ and half of the handshakes are duplicates

28 = N(N-1) / 2 ___ 56 = N(N-1) ___ 8 * 7 = N(N-1) ___ 8 = N

this can also be evaluated by using nC2 and solving for n
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