What is JotForm?
JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
At JotForm, we want to make sure that you’re getting the online form builder help that you need. Our friendly customer support team is available 24/7.
We believe that if one user has a question, there could be more users who may have the same question. This is why many of our support forum threads are public and available to be searched and viewed. If you’d like help immediately, feel free to search for a similar question, or submit your question or concern.
It is possible to achieve your requirement. You can take advantage of our "Conditions" feature to show / hide form fields based on the input/selection of another form field.
Please take a look at the following cloned form where I have added the required condition to show / hide the drop down field based on the selection of the check boxes: http://form.jotformpro.com/form/41531103084946?
Feel free to clone this form for a closer look. The following guide should help you in form cloning: http://www.jotform.com/help/42-How-to-Clone-an-Existing-Form-from-a-URL
Hope this helps.
Do get back to us if you have any questions.