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user 2096
For questions requesting examples of a certain structure or phenomenon
2
votes
Proofs without words
For $0 \lt k \lt n$,
$$\binom{n}{k} = \frac{n}{n-k}\binom{n-1}{k}$$
How k-subsets of [n], marked dark green in the rows, come from k-subsets of [n-1] after n-fold duplication and rearrangement:
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