Mathematics - (Combination|Binomial coefficient|n choose k)


Combination calculation called n choose k, because there are <math>\displaystyle n\choose k</math> ways to choose k elements from a set of n elements.

See also combinations, permutation calculator


  • Order doesn't matter (AB and BA are considered a single combination). If the order does matter it is a Permutation.
  • Repeat is not valid (AA is not a valid pair).


<MATH> \begin{array}{rrl} {n\choose k} & = & (n \text{ choose } k) & = & \frac{n!}{k!(n-k)!} \end{array} </MATH>


  • k is the trial number, k = 0, 1, …, n
  • n is the number total of trial


  • n would be the number of element in the whole set
  • k would be the number of elements in each combination

Documentation / Reference

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