Jinsi ya kukokotoa Combinations Permutations
Combinations Permutations ni nini?
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.
Mwongozo wa Hatua kwa Hatua
- 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
Mifano Iliyotatuliwa
Ingizo
Choose 3 from 10 (order matters)
Matokeo
720
P(10,3) = 10×9×8 = 720
Ingizo
Choose 3 from 10 (order irrelevant)
Matokeo
120
C(10,3) = 720/6 = 120
Ingizo
Lotto: 6 from 49
Matokeo
13,983,816
C(49,6)