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Combinations count ways to choose items where order does not matter. Permutations count ways where order does matter. Both use factorials and appear in probability, statistics, and combinatorics.
Guide étape par étape
- 1Permutations (order matters): P(n,r) = n! / (n−r)!
- 2Combinations (order irrelevant): C(n,r) = n! / (r!(n−r)!)
- 3Rule of thumb: if you can swap two items and get a different result, use permutations
Exemples résolus
Entrée
Choose 3 from 10 (order matters)
Résultat
720
P(10,3) = 10×9×8 = 720
Entrée
Choose 3 from 10 (order irrelevant)
Résultat
120
C(10,3) = 720/6 = 120
Entrée
Lotto: 6 from 49
Résultat
13,983,816
C(49,6)