public static long BinomialCoefficient(
	int n,
	int m
)

Public Shared Function BinomialCoefficient ( _
	n As Integer, _
	m As Integer _
) As Long

public:
static long long BinomialCoefficient(
	int n, 
	int m
)

Return Value

The binomial coefficient C(n,m) is the coefficient of x^m in the expansion of (1+x)ⁿ.

C(n,m) can also be given a combinatoric intrepretation as the total number of distinct subsets of m items in a set of n items.

Pascal's triangle is a classic representation of binomial coefficients.

The relation of an element in Pascal's triangle to its two parent elements is C(n+1,m) = C(n,m-1) + C(n,m). There are many other relationships among binomial coefficients. Among the most computationally useful is B(n,m+1) = (n-m)/(m+1) B(n,m), which can be used to generate all the binomial coefficients in a row of Pascal's triangle (i.e., all the coefficients for a given order polynomial) starting from an outer values B(n,0) = 1 =B(n,n). If you need a series of binomial coefficients, using a recurrion will be more computationally efficient than calling this method for each one.