Combinations Calculator (nCr)
Calculate combinations (nCr) and permutations (nPr) for any n and r. Supports large numbers via BigInt.
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Combinations (nCr, order does not matter)
13,983,816
C(49, 6) = 49! / (6! (49 - 6)!)
Permutations (nPr, order matters)
10,068,347,520
Frequently Asked Questions about the Combinations Calculator (nCr)
What is the difference between combinations and permutations?
Combinations (nCr) count selections where order does not matter, like picking lottery numbers. Permutations (nPr) count arrangements where order matters, like ranking finalists. nPr is always greater than or equal to nCr.
How do you calculate nCr?
The formula is nCr = n! / (r! (n-r)!). This calculator uses the iterative form nCr = product of (n-r+i)/i for i = 1 to r, which avoids huge intermediate factorials.
What are the odds of winning a 6-from-49 lottery?
C(49, 6) = 13,983,816, so a single ticket has roughly a 1 in 14 million chance of matching all six numbers.
When are combinations used in real life?
Lottery odds, poker hand counts, committee selection, A/B test groupings, and any problem where you choose a subset without caring about order.
Can this calculator handle very large numbers?
Yes. For n greater than 20, the calculator switches to BigInt arithmetic, so values like C(100, 50) compute exactly without losing precision.