The following are commonly adapted definition of Binomial Coefficients:

1.   A binomial coefficient C (n, k) has been defined as the coefficient of X^k in the expansion of (1 + X) ^n.

2.   A binomial coefficient C (n, k) can also give the number of ways, irrespective of order, that k objects can be chosen from among n objects; more clearly, the number of k-element subsets (or k-combinations) of an n-element set. 

This calculator will help you to compute the value of a binomial coefficient , given the values of the first non-negative integer n, and the second non-negative integer k.

You only need to enter the necessary parameter values in the corresponding tabs and then click on the ‘Calculate’ button.

The result gives you the binomial coefficient, that represents the number of unordered outcomes one can get after selecting k number of terms from a total sample space of n terms.

The formula used for calculating the binomial coefficient is:

C (n,k) = n!/(k!(n-k)!)

We take the factorial (same as in permutation and combinations) of n and divide it by the factorial of k and (n – k).

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