Ivan Shishkin, Rye (1878)

Problems/CombinatoricsReviewed

Binomial coefficient identity with a bijection

by Ancient Tree·
35
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
·
English
EnglishFrançais

Let nn be a positive integer and 1≤k≤n1\leq k \leq n. Show with a bijection that :

k(nk)=n(n−1k−1)k\binom{n}{k}=n\binom{n-1}{k-1}

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