With a 'normal' form, you'd have all the drop down boxes visible and populated from the start.
If you want a form that gradually displays new dropdown boxes based on the choises made so far, you have a couple of possibilities:
1) only PHP: You first create a form with the first drop down. The user makes a choice and sends the form. The PHP script receives the form values, and creates the new form based on the received values. Etc etc.