🔢Permutation vs Combination🎲
Both permutations and combinations count ways to choose items, but the answer depends on one question: does the order matter?
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🔢Permutation
- ✓Counts arrangements where order matters
- ✓ABC and CBA are counted as different
- ✓Always gives a count equal to or larger than combinations
- ✓Used for rankings, passwords and seat orders
- ✓Calculated as n! divided by (n minus r) factorial
🎲Combination
- ✓Counts selections where order does not matter
- ✓ABC and CBA are counted as the same group
- ✓Always gives a count equal to or smaller than permutations
- ✓Used for lottery picks, committees and card hands
- ✓Calculated by dividing permutations by r factorial
Verdict
Ask whether order matters. For a race podium (gold, silver, bronze) use permutations; for picking a committee where all members are equal, use combinations.
Frequently asked
How do I decide which to use?+
If rearranging the chosen items creates a different outcome, use permutations; if not, use combinations.
Is a lottery a permutation or a combination?+
A combination, because the order in which numbers are drawn usually does not matter.
Which gives a bigger number?+
Permutations, since each unordered combination corresponds to several ordered arrangements.
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