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.
دليل خطوة بخطوة
- 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
أمثلة محلولة
الإدخال
Choose 3 from 10 (order matters)
النتيجة
720
P(10,3) = 10×9×8 = 720
الإدخال
Choose 3 from 10 (order irrelevant)
النتيجة
120
C(10,3) = 720/6 = 120
الإدخال
Lotto: 6 from 49
النتيجة
13,983,816
C(49,6)