Does anyone have tips on how to better remember Pascal's identity? Ideally, I want to be able to recall it and the intuition quickly.
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9You can pick a team of $k$ by deciding that Draco Malfoy will definitely be in the team, and choosing his $k-1$ teammates, or by deciding Draco will definitely not be in the team, and choosing the $k$ members from among everyone else. So $\binom{n}{k} = \binom{n-1}{k-1}+\binom{n-1}{k}$. – Arturo Magidin Apr 27 '22 at 21:52
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5You can remember it by remembering how to build Pascal's Triangle (each entry being the sum of the two above it.) – Jair Taylor Apr 27 '22 at 21:56
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2@ArturoMagidin If you post your comment as an answer, I'll accept it. – FountainTree Apr 27 '22 at 22:08