N-Choose-K problem with recursion

gistfile1.php

<?php
/*
N-Choose-K problem solved with recursion
I decided to write this code after seeing this video https://www.youtube.com/watch?v=Hmld7MhFUDk

It can be easily executed at http://phpfiddle.org/
*/


function nChooseK ($n, $k, &$count, $_performanceFlag){
    $count++;
    if ($k>$n-1 || $k < 1) // if K is larger than N the function returns 0 because n,k: 1 <= k <= n-1 (See Wolframalpha or Google it, for example, https://en.wikipedia.org/wiki/Binomial_coefficient#Computing_the_value_of_binomial_coefficients)
        return 0;
    if (($k == 0) || ($n == $k)) // criteria based on the pascal triangle
        return 1;
    else if (($k == 1 || $n-1 == $k) && $_performanceFlag) // increases performance based on pascal triangle patterns
        return $n;
    else
        return nChooseK($n-1, $k-1, $count,$_performanceFlag) + nChooseK($n-1,$k,$count,$_performanceFlag);
        
}

/*
 Examples for C(20,5) and count of iteration to analize performance
 
 It can be compared with Wolfram Alpha at https://www.wolframalpha.com/input/?i=C(20,5)
*/

$count = 0;
echo "n-choose-k good performance: ".nChooseK(20,5, $count, true);
echo "<br>"."Iteration: ".$count;
$count = 0;  
echo "<br>"."<br>"."n-choose-k bad performance: ".nChooseK(20,5, $count, false);
echo "<br>"."Iteration: ".$count;
?>