"Title"

Given the definition of a mathematical combination:

where n is the total number of selections and r is the number you are choosing from the pool.

The formula for evaluation is:

What is the answer when you evaluate the following expression:

ok I admit I struggled with this one... I guess the main thing in understanding what the question is asking... a good place for information on this is HERE. Once you have an understanding of the functions you will need, I simply googled for a combination function: HERE
(I don't see a problem using code snippets like this as long as you understand them they are simply making your job easier, and there not solving it, just helping with a generic math function). then it's just a case of knowing what to add and subtract.

Awnser:

Source:

function fact( $num ){
   $res = 1;
   for ($i = 2; $i <= $num; $i++){
      $res *= $i;
   }
   return $res;
}
function perms( $n, $r ){
   if( $r > $n ){ return 0; }
   $i = 0;
   $res = 1;
   while( $i < $r ){
      $res = $res * $n;
      $i++;
      $n--;
   }
   return $res;
}
function combos( $n, $r ){
   if( $r > $n ){ return 0; }
   $res = perms( $n, $r );
   $res = $res / fact( $r );
   return $res;
} 


function solution(){
   $solution = combos(17, 10);
   $solution -= combos(30, 12);
   $solution += combos(50, 3);
   echo "= ".$solution."";
}