Permutations Calculator
P(n,r) — order matters
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.
- 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
Choose 3 from 10 (order matters)=720P(10,3) = 10×9×8 = 720
Choose 3 from 10 (order irrelevant)=120C(10,3) = 720/6 = 120
Lotto: 6 from 49=13,983,816C(49,6)
| Scenario | Type | Formula |
|---|---|---|
| Picking a PIN code | Permutation | P(10,4) = 5,040 |
| Lottery numbers | Combination | C(49,6) = 13,983,816 |
| Race podium (1st/2nd/3rd) | Permutation | P(n,3) |
| Committee selection | Combination | C(n,3) |
| Card hand (5 cards) | Combination | C(52,5) = 2,598,960 |
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Fun Fact
There are C(52,5) = 2,598,960 possible 5-card poker hands from a standard deck, but only 4 are Royal Flushes — odds of 1 in 649,740.
References
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