Submit button to filter data from table select by selecting on list select
Digging in, and trying to run some pseudo code it looks like there may be a problem with AJAX callbacks and tableselect fields regarding Drupal Core. 

https://www.drupal.org/node/1458824 (7x and 8x)

I would consider using the Views module with exposed filters.

You could fairly easily create a view that displays 2 articles, which exposes a state drop down list.  You could use a page or block view for the front end.

If you update your question with what you are ultimately trying to accomplish I can try to put together a more appropriate Views setup.