What is the meaning of adding $k$, and $1$, to $n$ in $\frac{(n+k-1)!}{{k!}{(n-1)!}}$, $C^i_{n,k}$, and how to visualise the components of this formula?
Here is my research:
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1Are you sure you mean $\frac{(n+k+1)!}{k!(n-1)!}$? Or is it $\frac{(n+k-1)!}{k!(n-1)!}$? – Haris Feb 02 '24 at 18:34
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1Can you clarify what the research image is describing? – peterwhy Feb 02 '24 at 18:39
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1https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics) – JMoravitz Feb 02 '24 at 18:40
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Thanks for the links, suggestions, and Stars and Bars! https://math.stackexchange.com/questions/1416132/proof-of-stars-and-bars-formula – Attila Vajda Feb 08 '24 at 19:39