$$ \left(\begin{array}{c}a+b\\ n\end{array}\right) = \sum_{i=0}^n \left(\begin{array}{c}a\\ k\end{array}\right) \left(\begin{array}{c}b\\ n-k\end{array}\right)$$
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This must be a duplicate, but I don't know how to find the link. – WhatsUp Dec 02 '19 at 18:30
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@WhatsUp a good way to start looking is by remembering the name for the identity. In this case, "Vandermonde's Identity" – JMoravitz Dec 02 '19 at 18:33
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Have you tried a combinatorial argument? – jl00 Dec 02 '19 at 18:34
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@JMoravitz Thanks, but I don't even remember the name ^_^ However, strangely I can remember how the proof goes... Human brains are quite interesting. – WhatsUp Dec 02 '19 at 18:35
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@JMoravitz thanks a lot – vanenshi Dec 02 '19 at 18:36