Combinations Permutations ಅನ್ನು ಹೇಗೆ ಲೆಕ್ಕ ಹಾಕುವುದು
Combinations Permutations ಎಂದರೇನು?
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.
ಹಂತ-ಹಂತದ ಮಾರ್ಗದರ್ಶಿ
- 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
Worked Examples
ಇನ್ಪುಟ್
Choose 3 from 10 (order matters)
ಫಲಿತಾಂಶ
720
P(10,3) = 10×9×8 = 720
ಇನ್ಪುಟ್
Choose 3 from 10 (order irrelevant)
ಫಲಿತಾಂಶ
120
C(10,3) = 720/6 = 120
ಇನ್ಪುಟ್
Lotto: 6 from 49
ಫಲಿತಾಂಶ
13,983,816
C(49,6)