• Haskell

binom n k = product [1+n-k..n] `div` product [1..k]

• C

long long binom(long long n, long long k){
  long long outp = 1;
  for(long long i = n - k + 1; i <= n; ++i) outp *= i;
  for(long long i = 2; i <= k; ++i) outp /= i;
  return outp;
}

• Clojure

(defn binom [n k]
  (let [fact #(apply * (range 1 (inc %)))]
    (/ (fact n)
       (* (fact k) (fact (- n k))))))

• C#

public BigInteger binom(int n, int k)
{
	return factorial(n)/(factorial(k) * factorial(n-k));
}

public BigInteger factorial(int x)
{
	BigInteger result = 1;
	for(int i=1;i<=x;i++)
	{
	result = result * i;
	}
	return result;
}

• D

BigInt binom(uint n, uint k)
{
   assert(n >= k);
   BigInt r = 1;
   for(uint i = 0; i <= k; ++i)
   {
      r *= n-i;
      r /= i+1;
   }
   return r;
}

• Dart

int binom(int n, int k) {
  int result = 1;
  for (int i = 0; i < k; i++) {
    result = result * (n - i) ~/ (i + 1);
  }
  return result;
}

• Fortran

integer, parameter :: i8 = selected_int_kind(18)
integer, parameter :: dp = selected_real_kind(15)
n = 100
k = 5
print *,nint(exp(log_gamma(n+1.0_dp)-log_gamma(n-k+1.0_dp)-log_gamma(k+1.0_dp)),kind=i8)

• Go

z := new(big.Int)
z.Binomial(n, k)

• JS

const fac = x => x ? x * fac (x - 1) : x + 1
const binom = (n, k) => fac (n) / fac (k) / fac (n - k >= 0 ? n - k : NaN)

• Java

static BigInteger binom(int N, int K) {
    BigInteger ret = BigInteger.ONE;
    for (int k = 0; k < K; k++) {
        ret = ret.multiply(BigInteger.valueOf(N-k))
                 .divide(BigInteger.valueOf(k+1));
    }
    return ret;
}

• PHP

gmp_binomial($n, $k);

• Pascal

var
  N, K, Res: TValue;
begin
  Res := BinomN(N, K);
end.

• Perl

sub binom {
  my ($n, $k) = @_;
  if ($k > $n - $k) { $k = $n - $k }
  my $r = 1;
  for ( my $i = $n/$n ; $i <= $k;) {
    $r *= $n-- / $i++
  }
  return $r
}

• Perl

sub binom {
   my ($n, $k) = @_;
   my $fact = sub {
      my $n = shift;
      return $n<2 ? 1 : $n * $fact->($n-1);
   };
   return $fact->($n) / ($fact->($k) * ($fact->($n-$k)));
}

• Python

def binom(n, k):
    return math.factorial(n) // math.factorial(k) // math.factorial(n - k)

• Python

def binom(n, k):
    return math.comb(n, k)

• Ruby

def binom(n,k)
  (1+n-k..n).inject(:*)/(1..k).inject(:*)
end

• Rust

fn binom(n: u64, k: u64) -> BigInt {
    let mut res = BigInt::one();
    for i in 0..k {
        res = (res * (n - i).to_bigint().unwrap()) /
              (i + 1).to_bigint().unwrap();
    }
    res
}