How to Calculate Combinations (nCr)

What is Combinations (nCr)?

Combinations (nCr) count the ways to choose r items from n when order does not matter. Fundamental in probability, statistics, and combinatorics.

Formula

C(n,r) = n! / (r! × (n−r)!)

C: C(n — C(n

Step-by-Step Guide

1C(n,r) = n! / (r! × (n−r)!)
2Order does NOT matter (unlike permutations)
3C(n,r) = C(n,n−r) — symmetrical property
4C(n,0) = C(n,n) = 1 always

Worked Examples

Input

Choose 3 from 10

Result

C(10,3) = 120 combinations

Frequently Asked Questions

What is Combinations?

Combinations (nCr) count the ways to choose r items from n when order does not matter. Fundamental in probability, statistics, and combinatorics

How accurate is the Combinations calculator?

The calculator uses the standard published formula for combinations. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Combinations calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Combinations calculator use?

The core formula is: C(n,r) = n! / (r! × (n−r)!). Each step in the calculation is shown so you can verify the result manually.

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