Combination & Permutation Calculator
Calculate combinations (nCr) and permutations (nPr) — how many ways to choose or arrange r items from n.
Combinations (nCr)
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Permutations (nPr) —
n! —
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How it works
nCr = n! ÷ (r!(n−r)!); nPr = n! ÷ (n−r)!Frequently Asked Questions
What is the difference between a combination and a permutation?
Order. A permutation counts arrangements (1st, 2nd, 3rd place from 8 runners = 336), a combination counts selections where order doesn't matter (choosing 3 of 8 = 56). Permutations are always more numerous.
When do I use nCr vs nPr?
Use nCr (combinations) for picking a group where order is irrelevant — lottery numbers, a committee. Use nPr (permutations) when the order matters — rankings, passwords, seating.
How many combinations in a lottery?
Choosing 6 numbers from 49 is 49C6 = 13,983,816 combinations — which is why the odds are so long. Enter n=49, r=6 to see it.