learn.howToCalculate
learn.whatIsHeading
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.
ステップバイステップガイド
- 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
解いた例
入力
Choose 3 from 10 (order matters)
結果
720
P(10,3) = 10×9×8 = 720
入力
Choose 3 from 10 (order irrelevant)
結果
120
C(10,3) = 720/6 = 120
入力
Lotto: 6 from 49
結果
13,983,816
C(49,6)