$sql="SELECT count( * ) AS count
FROM wp_posts
INNER JOIN wp_term_relationships ON wp_posts.ID = wp_term_relationships.object_id
INNER JOIN wp_term_taxonomy ON wp_term_relationships.term_taxonomy_id = wp_term_taxonomy.term_taxonomy_id
INNER JOIN wp_terms ON wp_term_taxonomy.term_id = wp_terms.term_id
WHERE wp_terms.term_id =".$key->term_id."
AND wp_term_taxonomy.taxonomy = 'category'";