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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.
Hướng dẫn từng bước
- 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
Ví dụ có lời giải
đầu vào
Choose 3 from 10 (order matters)
Kết quả
720
P(10,3) = 10×9×8 = 720
đầu vào
Choose 3 from 10 (order irrelevant)
Kết quả
120
C(10,3) = 720/6 = 120
đầu vào
Lotto: 6 from 49
Kết quả
13,983,816
C(49,6)