Binomial Coefficient Calculator (nCr)

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Combinations: choosing a committee of 3 from 10 (order irrelevant). Permutations: arranging 3 people in 3 ranked seats (order matters).
The total number of items in the set. Must be a non-negative integer, max 1000 for this tool.
How many items are selected from the set. Must be between 0 and n.
C(n,k) - CombinationsManageable count
120

Ways to choose k items from n when order does not matter

C(n+k-1,k) - With repetition220
C(n, n-k) - Complement120
Pascal's triangle row n1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1
Combinations C(n,k)120
Complement C(n,n-k)120
With repetition C(n+k-1,k)220

C(10,3) = 120

  • There are 120 ways to choose 3 items from 10 when order does not matter.
  • C(10,3) = C(10,7) = 120: choosing 3 items is equivalent to choosing which 7 items to leave out.
  • If repetition is allowed (e.g. a dice roll), the count becomes C(12,3) = 220.

Next stepTo list every combination, see a combinations-generator tool; for probability use this count as the denominator.

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