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Free combinations calculator for nCr problems. Count how many ways to choose items from a set without order, with exact large-number output and readable approximation.
Last updated: April 20, 2026
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Exact value
120
Readable approximation
120
n
10
r
3
Interpretation
There are 120 ways to choose 3 items from 10 items without regard to order.
Formula:
nCr = n! / (r! × (n - r)!)
Use combinations when order does not matter. Use permutations when order matters.
Use case
Team selection, subsets, lottery picks
Formula
nCr = n! / (r!(n-r)!)
Output
Exact + Approx format
n = 10, r = 3
Exact combinations
120
Approximation
120
The calculator applies the nCr formula and uses a multiplicative integer-safe method to avoid precision loss in large calculations. This enables exact results for many practical combinatorics scenarios.
nCr = n! / (r!(n-r)!)Combination values are symmetric: nCr = nC(n-r), which reduces computation cost for large n.
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