Saturday, 12 October 2019

How do I do combinatoric algebra without tedious factorial multiplication and division?

I find combinatoric algebra very non-intuitive. I'm talking about Pascal's Identity nr,
\binom{n+1}{r}=\binom{n}{r}+\binom{n}{r-1}.




I understand the tedious proof of the theorem but what's a trick for understanding combinatoric algebra in general? I can't eyeball and decompose a binomial without memorizing the formulas or doing tedious factorial multiplication and division.



It's never obvious how combinatoric algebra works:



EXample: enter image description here

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