I've been searching for the right way to count all published posts but excluding specific categories. I know of the function wp_count_posts but it doesn't have the option to exclude specific categories. So I came up with the following:

<?php
$categories = get_categories('exclude=1,2,3');
  foreach($categories as $category) {
    $total += $category->count;  
  }
echo $total;
?>

It works! But is that the correct way or is there some other way I'm missing?