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Permutations (ⁿPᵣ — order matters)
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Combinations (ⁿCᵣ — order ignored)
Permutations count ordered arrangements (ⁿPᵣ = n! ÷ (n−r)!); combinations count unordered selections (ⁿCᵣ = n! ÷ (r!·(n−r)!)). Very large results are shown in scientific notation.
Frequently Asked Questions
What is the difference between a permutation and a combination?
A permutation counts arrangements where order matters (e.g. a race podium), while a combination counts selections where order does not matter (e.g. a lottery draw). ⁿPᵣ is always greater than or equal to ⁿCᵣ.
How are they calculated?
ⁿPᵣ = n! ÷ (n−r)! and ⁿCᵣ = n! ÷ (r! × (n−r)!), where n is the total number of items and r is how many are chosen. Both require n ≥ r ≥ 0.
Calculate permutations (ⁿPᵣ) and combinations (ⁿCᵣ) for choosing r items from n.