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Permutations

A permutation of a set of distinct objects is an ordered arrangement of these objected.

For a set of \(n\) objects, there exists \(n!\) permutations of these.

Note: this is different to an unordered arrengement, which are Combinations.

k-permutations

To find permutations of \(k\) objects within a set of \(n\), an k-permutation can be caluculated.

Given \(n, k\) where \(0 \leq k \leq n\). There are \[ P(n,k)=n(n-1)\ldots(n-k+1) = \frac{n!}{(n-k)!} \]