Combinations Permutationsని ఎలా లెక్కించాలి
Combinations Permutations అంటే ఏమిటి?
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.
దశల వారీ గైడ్
- 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
పరిష్కరించిన ఉదాహరణలు
ఇన్పుట్
Choose 3 from 10 (order matters)
ఫలితం
720
P(10,3) = 10×9×8 = 720
ఇన్పుట్
Choose 3 from 10 (order irrelevant)
ఫలితం
120
C(10,3) = 720/6 = 120
ఇన్పుట్
Lotto: 6 from 49
ఫలితం
13,983,816
C(49,6)