Custom taxonomy post count

functions.php

<?php

function catCount($slug){

    global $wpdb;
	$query = "
		SELECT COUNT( DISTINCT cat_posts.ID ) AS post_count
		FROM gh_term_taxonomy AS cat_term_taxonomy INNER JOIN gh_terms AS cat_terms ON
		cat_term_taxonomy.term_id = cat_terms.term_id
		INNER JOIN gh_term_relationships AS cat_term_relationships 
		ON cat_term_taxonomy.term_taxonomy_id = cat_term_relationships.term_taxonomy_id
		INNER JOIN gh_posts AS cat_posts 
		ON cat_term_relationships.object_id = cat_posts.ID
		WHERE cat_posts.post_status = 'publish' 
		AND	cat_posts.post_type = 'product' 
		AND	cat_term_taxonomy.taxonomy = 'product_cat' 
		AND	cat_terms.slug = ('$slug')
	";
	return $wpdb->get_var($query);

}