How can I count the number of dropbox being filled?

I have 8 dropboxes with 4-5 selections in each dropbox. 

If 5 out of the 8 dropbox has selection, I would like to get a count of 5. How can this be done efficiently? 

My immediate makeshift solution: 

- 8 different number field equivalent to each of the dropbox.

- for each dropbox is filled, put the value of 1 into each of its corresponding number

- each just add all these 8 different number fields. 

But this is really a workaround though. Any advice?

The makeshift method works... .but I wonder if you may provide me a more elegant solution to this? 

That's actually a great workaround. I have tried others by not using number fields but I couldn't get them to work.

I think that's the only way to achieve that. Just hide the number fields so they won't appear in the live form.