binomial

binomial (n, k)

The binomial function returns the ratio:

$$\displaystyle \frac{n!}{k!(n-k)!}$$

It is assumed that n and k are integers and 0 <= k <= n and ! denotes the factorial function.

When k>n, the binomial function returns 0. If either n or k are singular (i.e., NaN or INF), the binomial function returns NaN.

Note that while the binomial function is an integer-valued function, a double-precision number has 53 bits for the mantissa. This means that numbers over 2⁵² (about 4.5x10¹⁵) will be accurate to about one part in 2x10¹⁶.

If you encounter overflow you can use the APMath operation to obtain the result. For example:

Print factorial(1000)
  inf
APMath/V result = factorial(1000)
  4.02387260077093773543702433923003985719374864210715E+2567