function binomial_coefficient ($n, $k)
{
  //variable and initializations
  $the_result = 0;
  $n_factorial = 0;
  $k_factorial = 0;
  $n_k_factorial = 0;

  //calculate n,k n-k factorial
  $n_factorial = factorial_integer($n);
  $k_factorial = factorial_integer($k);
  $n_k_factorial = factorial_integer($n - $k);

  if ($n_factorial != "error" and
      $k_factorial != "error" and
      $n_k_factorial != "error")
  {
    $the_result = $n_factorial / ($k_factorial * $n_k_factorial);
  }
  else
  {
    return "error";
  }

  return $the_result;
}

function factorial_integer ($k)
{
  //variable and initializations
  $the_result = 1;

  //check to see if k is an integer
  if (!is_int($k))
  {
    return "error";
  }

  //check for k < 0
  if ($k < 0)
  {
    return "error";
  }

  //0! = 1
  if ($k == 0)
  {
    return 1;
  }

  //calculate the result
  for ($i = 2; $i <= $k; $i++)
  {
    $the_result = $the_result * $i;
  }

  //return the value
  return $the_result;
}

<?
include ("ajstatistics.php");
$n = 6;
$k = 3;

$the_binomial_coefficient = binomial_coefficient($n, $k);

echo "n = $n<br>";
echo "k = $k<br>";
echo "the_binomial_coefficient = $the_binomial_coefficient<br>";
?>