כיצד לחשב את Combinations Permutations
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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.
מדריך שלב אחר שלב
- 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
קלט
Choose 3 from 10 (order matters)
תוצאה
720
P(10,3) = 10×9×8 = 720
קלט
Choose 3 from 10 (order irrelevant)
תוצאה
120
C(10,3) = 720/6 = 120
קלט
Lotto: 6 from 49
תוצאה
13,983,816
C(49,6)