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The binomial coefficient is the number of ways of picking unordered outcomes from possibilities, also known as a combination or combinatorial number. therefore gives the number of k-subsets possible out of a set of distinct items. For example, The 2-subsets of are the six pairs , , , , , and , so . The number of lattice paths from the origin to a point ) is the binomial coefficient (Hilton and Pedersen 1991).
In mathematics, binomial coefficients are represented as \(\binom{a}{b}\), where \(a\) is the \((a+1)^{\text{th}}\) row, and \(b\) is the \((b+1)^{\text{th}}\) number in that row, counting from the left, acting as an index.