Evaluate binomial coefficients

Evaluate binomial coefficients
You are encouraged to solve this task according to the task description, using any language you may know.

This programming task, is to calculate ANY binomial coefficient.

This formula is recommended:

${\binom {n}{k}}={\frac {n!}{(n-k)!k!}}$

C++

<lang cpp>double Factorial(double nValue)

  {
      double result = nValue;
      double result_next;
      double pc = nValue;
      do
      {
          result_next = result*(pc-1);
          result = result_next;
          pc--;
      }while(pc>2);
      nValue = result;
      return nValue;
  }

double EvaluateBinomialCoefficient(double m_nValue, double nValue)

  {
      double result;

      result = (Factorial(m_nValue))/(Factorial(nValue)*Factorial((m_nValue - nValue)));
      nValue = result;
      return nValue;
  }</lang>

Tcl

This uses exact arbitrary precision integer arithmetic. <lang tcl>package require Tcl 8.5 proc binom {n k} {

   # Compute the top half of the division; this is n!/(n-k)!
   set pTop 1
   for {set i $n} {$i > $n - $k} {incr i -1} {

set pTop [expr {$pTop * $i}]

   }

   # Compute the bottom half of the division; this is k!
   set pBottom 1
   for {set i $k} {$i > 1} {incr i -1} {

set pBottom [expr {$pBottom * $i}]

   }

   # Integer arithmetic divide is correct here; the factors always cancel out
   return [expr {$pTop / $pBottom}]

}</lang> Demonstrating: <lang tcl>puts "60_C_30 = [binom 60 30]"</lang> Output:

60_C_30 = 118264581564861424