About nCr Combinatorics Calculator
Combinations count the ways to choose r items from n when order does not matter: nCr = n! ÷ (r! × (n − r)!). Permutations count ordered selections: nPr = n! ÷ (n − r)!. The factorial n! is the product of every whole number from 1 to n. This calculator uses exact big-integer arithmetic, so results are never rounded. Both inputs must be whole numbers with 0 ≤ r ≤ n ≤ 1,000, without repetition.
How to use nCr Combinatorics Calculator
- Fill in "n" and "r".
- The result appears below and updates as you type.
- Copy the result with the copy button, or download it as a file where that is offered.
Questions about nCr Combinatorics Calculator
What is the difference between a combination and a permutation?
In a permutation the order of the chosen items matters, in a combination it does not. Picking 3 of 10 people for a committee gives 120 combinations, while filling 3 ranked positions gives 720 permutations.
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