Permutations (ordered arrangements) and combinations (unordered selections)
Specialist Mathematics · Unit 1 — Combinatorics, proof, vectors and matrices · Combinatorics
Learning objectives (10)
LO-1Define and use combinations.LO-2Define and use permutations.LO-3Model and solve problems that involve permutations and combinations including probability problems, with and without technology. Specialist Mathematics 2025 v1.4LO-4Solve problems that involve combinations with restrictions including specific objects grouped together and selection from multiple groups.LO-5Solve problems that involve combinations.LO-6Solve problems that involve permutations with restrictions including repeated objects, specific objects grouped together and selection from multiple groups.LO-7Solve problems that involve permutations.LO-8Use factorial notation.LO-9Use the notation (𝑛 𝑟) and 𝐶𝑟 𝑛 to represent the number of ways of selecting 𝑟 objects from 𝑛 distinct objects where order is not important. 𝐶𝑟 𝑛 = (𝑛 𝑟) = 𝑛! 𝑟!(𝑛−𝑟)!LO-10Use the notation 𝑃𝑛 𝑟 to represent the number of ways of selecting 𝑟 objects from 𝑛 distinct objects where order is important. 𝑃𝑟 𝑛 = 𝑛! (𝑛−𝑟)! = 𝑛 × (𝑛 − 1) × (𝑛 − 2) × … × (𝑛 − 𝑟 + 1)
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