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.