Monthly Archives: November 2020

Cheat Sheet for Distributing $k$ Balls into $n$ Boxes

Distribution of Restriction $k\text{ Balls}$ $n\text{ Boxes}$ None $\le 1$ $\ge 1$ $=1$ $distinct$ $distinct$ $$n^k$$ $$(n)_k$$ $$n!S(k,n)$$ $$n!\text{ or }0$$ $identical$ $distinct$ $${n+k-1}\choose k$$ $$n\choose k$$ $${k-1}\choose{n-1}$$ $$1\text{ or }0$$ $distinct$ $identical$ $$\sum_{i=1}^{n}S(k,i)$$ $$1\text{ or }0$$ $$S(k,n)$$ $$1\text{ or … Continue reading

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