I have never seen a website with check boxes in a drop down list before. I don't think it can be done because normally when you see a drop down list, you simply make the choice in the drop down list then click the submit button to submit the data to a page your using to process the info. if you tried to use a check box in a drop down list you would be placing a form field inside another form field. It would be like double sending the same choice using the same submit button. It would be like trying to hammer a 1 nail into the wall with 2 hands with a hammer in each hand. each hand would just get in the way of each other.
Perhaps you should consider a different layout design, such as an unordered list. By the way, questions like this should not go in the PHP section.