Calculate the number of ways to choose items from a set.
Parameters
Possibilities
Combinations (nCr)120Order doesn't matter
Permutations (nPr)720Order matters
Mathematical Insights
Ratio (P/C)6
Difference600
About this calculator
Overview
Combinations and permutations are ways to calculate the number of possible outcomes in a given scenario. Permutations are used when the order of the outcomes matters, while combinations are used when the order does not matter.
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Pro Tips
Use Combinations for groups or sets where order is irrelevant (e.g., choosing a committee).
Use Permutations for arrangements where order is key (e.g., race results, PIN codes).
If n = r, there is only 1 combination, but r! permutations.
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Fun Facts
"There are 52! ways to shuffle a deck of cards. That's 8.06e67, which is more than the number of atoms in the Milky Way!"
"A 'combination' lock is actually a 'permutation' lock because the order of numbers matters."
"The number of permutations will always be greater than or equal to the number of combinations for the same n and r."
