



 
Hi Nazrul, Suppose there were $n$ people at the party including you and me. I shook hands with $n1$ people, so did you and so did everyone else at the party. Thus it looks like there were $n(n  1)$ handshakes but this included you shaking hands with me and me shaking hands with you. In fact it counts each handshake twice so there are actually $\large \frac{n(n  1)}{2}$ handshakes. Can you complete the problem now? Can you do it without solving a quadratic? Penny  


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