# Binomial Coefficient

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## Definition: Binomial Coefficient

Binomial coefficients, denoted as nCr , is the number of ways in which ‘r’ items can be chosen from a set of ‘n’ items. They are a collection of positive integers that occur as coefficients in the binomial theorem. It is the number of ways of picking ‘r’ unordered outcomes from ‘n’ possibilities.

Its value is given by:-

nCr =n!/r!(n-r)!           0≤k≤n

The binomial coefficient can be arranged to form Pascal’s triangle. It is obtained by arranging binomial coefficients into rows for successive values of n, and in which r ranges from 0 to n. Hence, this concludes the definition of Binomial Coefficient along with its overview.

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