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IA: Handshake Problem

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I'm currently thinking of a good topic for my Math Exploration, and I decided to take "The Handshake Problem" as my topic. However, I do not know exactly how to outline/start my IA. Like, i was thinking of applying the "N choose R" in it because we actually discussed that in class. But, I don't know how to make my IA even more sophisticated from then on. I was also thinking of applying this in a more practical sense, like "how many handshakes in a certain country," but isn't that too simple because i will simply just use the formula? Or, how should I explore the exponential growth (curved graph) of the increasing values of the handshake problem? But, I don't exactly know what to explore in that, and it's quite too simple because i will just simply graph.

I really need help. Hope anyone out there can help me deepen and structure my essay. Thank you very much in advance! :)

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Sounds like it's too simple, to be honest. The solution of the handshake problem can be modeled using a quadratic function, so you do know how the values increase with larger values. The maths behind it would end up being rather simple (including the proof of the general case),

For expanding it, two ideas come to mind. I can't say if they are feasible/appropriate or not, but you could consider other situations where this may be used, or looking to generalize the result with 3-way handshakes or more.

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