Counting Specific Posts

<?php
$num_posts = wp_count_posts( 'post' );
echo '<p>Number of private posts: '.$num_posts->publish. '</p>';

$tag = 'food';
$taxonomy = 'post_tag';
$term = get_term_by('name', $tag, $taxonomy);
if ($term) {
  $tagposts = get_objects_in_term(array($term->term_id), $taxonomy);
}
if ($tagposts) {
  echo '<p>Number of posts with tag '.$tag .': '.count($tagposts). '</p>';
}

$myposts = null;
$metakey = 'your_custom_field_key';
$args=array(
  'meta_key' => $metakey,
  'post_type' => 'post',
  'post_status' => 'publish',
  'showposts' => -1,
  'caller_get_posts'=> 1
);
$myposts = get_posts($args);
if ($myposts) {
  echo '<p>Number of posts with metakey '.$metakey .': '.count($myposts). '</p>';
}

?>

Thank you for your help.

But how do I implement a limitation towards a specific category?

Ah, new and possibly unclear requirements, but how about this.

$tag = 'mycategory';
$taxonomy = 'category';
$term = get_term_by('name', $tag, $taxonomy);
if ($term) {
  $tagposts = get_objects_in_term(array($term->term_id), $taxonomy);
}
if ($tagposts) {
  echo '<p>Number of posts with catgory '.$tag .': '.count($tagposts). '</p>';
}

Thank you. Here is the result but I cant get it to search for multiple values.

function count_in_factory_in_category($searchcat_id)
{
	global $post;

	$factory_posts = null;
	$metakey = 'status';
	$args = array(
	  'meta_key' => $metakey,
	  'meta_value' => array('completed', 'in production', 'in development', 'archived'),
	  'post_type' => 'post',
          'post_status' => 'publish',
	  'cat' => $searchcat_id,
	  'showposts' => -1,
	  'caller_get_posts'=> 1
	);

	$factory_posts = get_posts($args);
	if ($factory_posts)
	{

	   $infactory_result = count($factory_posts);
	   $category_url = get_category_link($searchcat_id);

	   	if(is_user_logged_in())
		{
echo '	<div>
			<p class="hits">';

		/* if we have results that is more then 0 then insert the category link */
		if($infactory_result != 0)
 		{
                echo '<a href="'.$category_url.'" title="">'.$infactory_result.'</a>';
 		/* otherwise empty to hide this box */
 		} else { echo '&nbsp;'; }
echo '		</p>
 		</div> ';
 	 	}

	}
}

Try 'category__in'=> array($searchcat_id),

And this will not work:
'meta_value' => array('completed', 'in production', 'in development', 'archived'),

might want to look at Displaying_Posts_Using_a_Custom_Select_Query

Thank you, that solved it.

Working example is here.