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Probability Calculators

Combination Calculator

Number of ways to choose r items from n when order does not matter (nCr), with and without repetition.

Enter values

Results update as you type.

Result

C(n, r)

120

With repetition C(n + r − 1, r)
220
Step-by-stepShow
  1. C(10, 3) = 10! ÷ (3! × 7!) = 120

About the Combination Calculator

Number of ways to choose r items from n when order does not matter (nCr), with and without repetition.

Also known as: ncr calculator, n choose r, combinations formula, binomial coefficient.

How to use this calculator

  1. Enter total items n, chosen r.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Open “Step-by-step” to see how the answer was worked out.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

C(n, r) = n! / (r!(n − r)!)

Worked example

Using the values pre-filled in the calculator above:

  • Total items n = 10
  • Chosen r = 3

the calculator returns:

  • C(n, r): 120
  • With repetition C(n + r − 1, r): 220

Working

  1. C(10, 3) = 10! ÷ (3! × 7!) = 120