Combination Calculator

Find the number of combinations — ways to choose r items from n when order does not matter. Enter n and r.

n (total items)

r (chosen)

Combinations

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Order does not matter.

Usage Tip

Choosing 3 from 10 is the same as leaving out 7 from 10 — that is why C(10,3) equals C(10,7).

THE MATH

C(n, r) = n! ÷ (r! × (n − r)!)
Order does not matter

Combinations count selections where order is irrelevant, like picking a committee or lottery numbers.
They are permutations divided by the number of orderings of each group.

Enter whole numbers with r no greater than n.
The matching permutation count is shown for comparison.
C(n, r) equals C(n, n − r).

The calculators and tools on Formula Factory are provided for general guidance and informational purposes only. Results are estimates based on standard formulas and the values you enter — they do not constitute professional engineering, electrical, or architectural advice. Always verify calculations with a qualified professional before making decisions for any safety-critical, code-compliance, or commercial application. Formula Factory makes no representations or warranties as to the accuracy or completeness of any result, and accepts no liability for errors, omissions, or any outcomes arising from reliance on this information.