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@jemoka / Jemoka Knowledge Base / wiki/concepts/permutation.md
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--- title: "permutation" type: concept related: [Permutation] source: https://www.jemoka.com/posts/kbhpermutation/ confidence: high status: active --- A permutation \(\pi\) of some \(\{1,2,…, n\}\) is a rearrangement of this list. There are \(n!\) different permutations of this set. A permutation is an ORDERED arrangement of objects. permutation with indistinct objects What if you want to order a set with sub-set of indistinct objects? Like, for instance, how many ways are there to order: \begin{equation} 10100 \end{equation} For every permutation of \(1\) in this set, there are two copies being overcounted. Let there are \(n\) objects. \(n_1\) objects are the indistinct, \(n_2\) objects are indistinct, … \(n_{r}\) objects are the same. The number of permutations are: \begin{equation} \frac{n!}{{n_1}!{n_2}! \dots {n_r}!} \end{equation} You can use iterators to give you permutations.