Math
Combinations Calculator (nCr)
Calculate combinations (nCr) and permutations (nPr) for any n and r. Supports large numbers via BigInt.
Enter your values
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 3 toppings from a menu. Permutations (nPr) count arrangements where order matters, like awarding gold, silver, and bronze to 3 finalists. For any given n and r, nPr is always greater than or equal to nCr.
How do you calculate nCr?
The standard formula is nCr = n! / (r! x (n - r)!). This calculator uses an iterative form that computes the product of (n - k + i) / i for i from 1 to k, where k = min(r, n - r), so division stays exact at every step and no enormous intermediate factorials are needed.
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. Enter n = 49 and r = 6 to verify.
When are combinations used in real life?
Lottery odds, poker hand counts, committee selection, clinical trial group assignments, and any problem where you choose a subset without caring about order. If the arrangement of the chosen items matters, use the permutations result the calculator also returns.
Can this calculator handle very large numbers?
Yes. For n greater than 18, the calculator switches to BigInt arithmetic, so values like C(100, 50) = 100,891,344,545,564,193,334,812,497,256 compute exactly without any floating-point rounding.