Specialist Mathematics Β· Unit 1 Β· Combinatorics Β· Permutations (ordered arrangements) and combinations (unordered selections)

Use the notation 𝑃𝑛 π‘Ÿ to represent the number of ways of selecting π‘Ÿ objects from 𝑛 distinct objects where order is important. π‘ƒπ‘Ÿ 𝑛 = 𝑛! (π‘›βˆ’π‘Ÿ)! = 𝑛 Γ— (𝑛 βˆ’ 1) Γ— (𝑛 βˆ’ 2) Γ— … Γ— (𝑛 βˆ’ π‘Ÿ + 1)

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Use the notation (𝑛 π‘Ÿ) and πΆπ‘Ÿ 𝑛 to represent the number of ways of selecting π‘Ÿ objects from 𝑛 distinct objects where order is not important. πΆπ‘Ÿ 𝑛 = (𝑛 π‘Ÿ) = 𝑛! π‘Ÿ!(π‘›βˆ’π‘Ÿ)!
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