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    Shaking Hands Problem

    Module 3 Day 8 Challenge Part 3
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    • RZ923
      RZ923 M0★ M2★ M3★ M4★ M5 last edited by

      In the casework method, \(10+9+8+...+1\) looks very familiar... it's the famous shaking hands problem!
      Suppose you have 11 people shaking hands with each other, then it's \(10+9+...+1\) I'm pretty sure no explanation is needed.
      How about the stars ⭐ and bars 📊 method? It turns out you can explain it using the more "fancy" trick too!
      The number of ways to choose 2 out of 11 people to shake hands with each other is, well, \(\binom{11}{2}\).
      Same as the stars and bars grade curve problem!
      And if there are 4 grades, like in the mini-question...
      You will have 3 people shaking hands with each other at the same time!
      Weird, but true.

      Very Interesting

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