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.

Read more about this topic:  Binomial Coefficient

Famous quotes containing the word statistics:

    “O for a man who is a man, and, as my neighbor says, has a bone in his back which you cannot pass your hand through! Our statistics are at fault: the population has been returned too large. How many men are there to a square thousand miles in this country? Hardly one.”
    —Henry David Thoreau (1817–1862)