I need an order form that limits the total number of items to 7.

I need an order form that limits the total number of items to 7. I was using a form and just made a bunch of lines with each one an option. But our customers have a voucher that lets them order 7 things free, choosing from about 12. How can I allow them to choose 7 items only and respond to them if they have anything other than 7 selections? This page is not yet published.

If you only need to display your options then you could use a multiple choice field since it allows to set a max number of selections. 

Adding the field to your form: 

To limit the selections you only need to open the field properties and set the limits under the surveying tab: 

Please, give it a try and let us know if you have any question. 

But what if they want two or more of a single selection? Can the multiple choice form have a numerical input rather than a simple checkbox?

You could set up your options using individual number fields.  Total up the values in those fields using a calculation field:

https://www.jotform.com/help/259-How-to-perform-calculation-in-the-form

Then you can do something like conditionally show the submit button or a text field with a message based on the total:

https://www.jotform.com/help/316-How-to-Show-or-Hide-Fields-Base-on-User-s-Answer

Or you can even send different emails if you still want them to be able to submit the form with a total higher than 7:

https://www.jotform.com/help/167-How-to-Send-Email-Based-on-Selection

I made the calculations work.

I made the SUBMIT box an image and it will not appear until the TOTAL box says 7.

I made the HOVER TEXT for the total box say "the total must equal 7".

I was testing so I added more than I should which made the total more than 7. SO I DIRECTLY EDITED AND CHANGED TOTAL box TO 7, and it let me.

It did not change any of the other boxes from being wrong. IN FACT THE TOTAL NUMBER OF ITEMS IS WRONG BUT BECAUSE I DIRECTLY EDITED THE TOTAL BOX THE ENTIRE THING IS WRONG. It should never allow me to change the total box. That box should be absolutely connected to the boxes used to make the calculation.

While editing your calculation, click on "...":

From there, click the "Options" tab and select "Result field is read only":

OK, that part works now, too. Now I need to have the form show an error somehow if the total is EVER other than 7 during calculations input.

For instance, in the first box I enter 2, 2<7 so "error", maybe I need to have the hover text over the total line appear until all the input equals 7.

Easiest way to do this would be to show a text field with your error message if the total does not meet the requirements.  Using your example, a simple condition would be as follows:

With "Error Message" being a Text field with your error message text.

To prevent submitting the form, you could set up a condition like this: