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• Module 3 Day 8 Challenge Part 1

  Casework Solution

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• Module 3 Day 8 Challenge Part 2

  Stars and Bars Solution

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• Module 3 Day 8 Challenge Part 3

  Stars and Bars Solution

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  R

  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.

• Module 3 Day 8 Your Turn Part 1

  Pirates Splitting Gold (Casework Solution)

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• Module 3 Day 8 Your Turn Part 2

  Pirates Splitting Gold (Casework Solution)

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  B

  In the video, when Prof. Loh was explaining the second way to do the pirates and gold coins problem, he only took away 8 choose 3. I thought you should take away all the different cases like 7 choose 3, 6 choose 3, etc. Why didn't he take away the rest? Thanks.