Robovito

<?php

// Config
$n_existing_stickers = 217;
$n_missing_stickers = 8;
$n_packages = 500;
$n_stickers_per_package = 5;
$iterations = 1000;

$stickers = range(0, $n_existing_stickers);

$success_counter = 0;
for($iteration=0; $iteration<$iterations; $iteration++){
  $missing_stickers = range(0, $n_missing_stickers);

  // Generates packages
  $packages = [];
  for($i=0; $i<$n_packages; $i++) {
    shuffle($stickers);
    $packages[] = array_slice($stickers, 0, $n_stickers_per_package);
  }

  // Search for stickers
  foreach($packages as $package){
    $missing_stickers = array_diff($missing_stickers, $package);
  }

  if(!count($missing_stickers)) $success_counter++;
}
echo "Iterations: {$iterations}\n";
echo "Successes:  {$success_counter}\n";