Binomial Coefficient - Combinatorics and Statistics

Combinatorics and Statistics

Binomial coefficients are of importance in combinatorics, because they provide ready formulas for certain frequent counting problems:

  • There are ways to choose k elements from a set of n elements. See Combination.
  • There are ways to choose k elements from a set of n if repetitions are allowed. See Multiset.
  • There are strings containing k ones and n zeros.
  • There are strings consisting of k ones and n zeros such that no two ones are adjacent.
  • The Catalan numbers are
  • The binomial distribution in statistics is
  • The formula for a Bézier curve.

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