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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.
Пошаговое руководство
- 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
Решённые примеры
Ввод
Choose 3 from 10 (order matters)
Результат
720
P(10,3) = 10×9×8 = 720
Ввод
Choose 3 from 10 (order irrelevant)
Результат
120
C(10,3) = 720/6 = 120
Ввод
Lotto: 6 from 49
Результат
13,983,816
C(49,6)