Suggest an editImprove this articleRefine the answer for “What does an "arrangement" mean in combinatorics?”. Your changes go to moderation before they’re published.Approval requiredContentWhat you’re changing🇺🇸EN🇺🇦UAPreviewTitle (EN)Short answer (EN)An **arrangement** in combinatorics is a way to **select and order** elements from a set. **Key point:** an arrangement of k out of n is an ordered selection of k distinct elements taken from n distinct elements: elements are not repeated, and order matters.Shown above the full answer for quick recall.Answer (EN)ImageAn **arrangement** in combinatorics is a way to **select and order** elements from a set. ### Formal definition An **arrangement of** ***n*** **taken** ***k*** **at a time** is an **ordered selection** of *k* distinct elements taken from *n* distinct elements. Key words: - elements are **not repeated**; - **order matters**. ### Example Suppose there are 3 elements: `{A, B, C}`. Arrangements of 2: - AB - BA - AC - CA - BC - CB Total: A32=3!(3−2)!=6A_3^2 = \frac{3!}{(3 - 2)!} = 6A32=(3−2)!3!=6 ### Difference from other concepts | Concept | What matters | |---|---| | **Combination** | order **does not matter** | | **Arrangement** | order **matters** | | **Permutation** | **all elements** are used | ### In the context of algorithms Arrangements come up in tasks such as: - generating all variants of length `k` without repetition; - enumerating states while taking order into account; - brute-force solutions with a fixed sequence length. **Short version for an interview:** > An arrangement is an ordered selection of *k* distinct elements out of *n*: order matters, no repetitions.For the reviewerNote to the moderator (optional)Visible only to the moderator. Helps review go faster.