Can several JOIN clauses in a MySQL query exponentiate number of rows it has to check?

So I was on tech support with our host provider about slow database response that I'd been experiencing on a crucial search page and after some investigating he told me that the query that I'm using was checking 67,998,176 rows. Now the largest table that appears on this query has at most 116 rows and the rest of them have an average of 25 rows each.

Here's the SQL of my query

 SELECT COUNT( DISTINCT `A`.`id`) AS `total_num_resource_rows`
 FROM `admin_site_resources` AS `A`
 LEFT JOIN `admin_site_organization_resource` AS `B` ON `B`.`res_id`=`A`.`id`
 LEFT JOIN `admin_site_organizations` AS `C` ON `B`.`org_id`=`C`.`id`
 LEFT JOIN `admin_site_resource_res_topic` AS `D` ON `D`.`re开发者_高级运维source_id`=`A`.`id` 
 LEFT JOIN `admin_site_resource_topics` AS `E` ON `E`.`id`=`D`.`res_topic_id`
 LEFT JOIN `admin_site_resource_audience` AS `F` ON `F`.`resource_id`=`A`.`id`
 LEFT JOIN `admin_site_audiences` AS `G` ON `G`.`id`=`F`.`audience_id`
 LEFT JOIN `admin_site_resource_curriculum_topic` AS `H` ON `H`.`resource_id`=`A`.`id`
 LEFT JOIN `admin_site_curriculum_topics` AS `I` ON `I`.`id`=`H`.`curriculum_topic_id`
 LEFT JOIN `admin_site_resource_curriculum_grade` AS `J` ON `J`.`resource_id`=`A`.`id`
 LEFT JOIN `admin_site_curriculum_grades` AS `K` ON `K`.`id`=`J`.`curriculum_grade_id`
 LEFT JOIN `admin_site_resource_curriculum_subject` AS `L` ON `L`.`resource_id`=`A`.`id`
 LEFT JOIN `admin_site_curriculum_subjects` AS `M` ON `M`.`id`=`L`.`curriculum_subject_id` 
 LEFT JOIN `admin_site_resource_res_type` AS `N` ON `N`.`resource_id`=`A`.`id`
 LEFT JOIN `admin_site_resource_types` AS `O` ON `O`.`id`=`N`.`res_type_id` 
 LEFT JOIN `admin_site_resource_res_area_location` AS `P` ON `P`.`resource_id`=`A`.`id`
 LEFT JOIN `admin_site_resource_area_locations` AS `Q` ON `Q`.`id`=`P`.`res_area_location_id` 

 WHERE `A`.`post_status`='approved' AND (
`A`.`resource_name` LIKE '%alpha%'
OR `A`.`aliases` LIKE '%alpha%' 
OR `A`.`short_desc` LIKE '%alpha%' 
OR `A`.`resource_url` LIKE '%alpha%' 
OR `A`.`other_resource_type` LIKE '%alpha%' 
OR `C`.`org_name` LIKE '%alpha%' 
OR `E`.`topic_label` LIKE '%alpha%' 
OR `G`.`audience_label` LIKE '%alpha%' 
OR `I`.`topic_label` LIKE '%alpha%' 
OR `K`.`grade_label` LIKE '%alpha%' 
OR `M`.`subject_label` LIKE '%alpha%' 
OR `O`.`type_label` LIKE '%alpha%' 
OR `Q`.`area_location_label` LIKE '%alpha%' );

Yes, I understand this query is pretty long and ugly but I guess it's a result of all the normalization that had to be done for it. What I can't understand is how a few rows suddenly turned to almost 68 million rows. Are the LEFT JOINS to blame for this?

Depending on how many rows in each table match each join condition, you can have up to 116 rows from the first table, each paired with up to 116 rows from the second table (13456 rows now), each paired with up to 116 rows from the third table (1560896 rows now), each paired with up to 116 rows from the fourth table (181063936 rows now)... do you see where this is going?

You might only have 116 rows in that largest table, but when you take every combination of 16 tables' keys... http://en.wikipedia.org/wiki/Combination

Rewrite it as:

 SELECT COUNT(*) AS `total_num_resource_rows`
 FROM `admin_site_resources` AS `A`
 WHERE `A`.`post_status`='approved' AND
   ( `A`.`resource_name` LIKE '%alpha%'
  OR `A`.`aliases` LIKE '%alpha%' 
  OR `A`.`short_desc` LIKE '%alpha%' 
  OR `A`.`resource_url` LIKE '%alpha%' 
  OR `A`.`other_resource_type` LIKE '%alpha%' 
  OR EXISTS ( SELECT * 
              FROM `admin_site_organization_resource` AS `B` 
                JOIN `admin_site_organizations` AS `C`
                  ON `B`.`org_id`=`C`.`id`
              WHERE `B`.`res_id`=`A`.`id`
                AND `C`.`org_name` LIKE '%alpha%' 
            )
  OR EXISTS ( 
             ...
            )
  OR EXISTS ( 
             ...
            )
  ...
    )