# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

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Concept guide



## [Permutations and combinations: proving P(n,k)=n!/(n−k)! and C(n,k)=n!/(k!(n−k)!) by counting](/en/derivations/derivation-mko-permutation-combination-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-permutation-combination)

Let X be a set of exactly n distinct objects, with natural numbers n, k and 0≤k≤n, and selection without replacement and without repetition. Prove that the number of ordered selections of k objects from X is P(n,k)=n!/(n−k)!, that the number of unordered selections is C(n,k)=n!/(k!(n−k)!), and that both equal 1 when k=0. Finally compute P(5,3)=60 and C(5,3)=10 for X={a,b,c,d,e} and k=3.

Permutations and combinations

derivation-mko-permutation-combination-01





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