PHP Manual: Calculates binomial coefficient

GMP gmp_binomial(GMPintstring $n, int $k)

Calculates the binomial coefficient C(n, k).

n: A GMP object, an int, or a string that can be interpreted as a number following the same logic as if the string was used in gmp_init with automatic base detection (i.e. when base is equal to 0).
k

Returns the binomial coefficient C(n, k).

Throws ValueError if k is negative. Prior to PHP 8.0.0, E_WARNING was issued instead.

Version	Description
8.0.0	This function no longer returns `false` on failure.