Just count them. It’s as simple as that. You only need to count the files that need mixing. You may decide to group somethings like backing vocals together and send them as one stereo file. This is OK, but obviously I can only mix them as a group from that point on wards (panning, level and processing are already baked in at this point), so make sure you get it right at your end.
You don’t need to count duplicate files. There’s more on this in the section (how to prepare my files for mixing). Example, you may have a reverb on a sound that you think works, so you send that file for mixing. But you may also choose to send that file without the reverb, just in case it doesn’t work and I have to tweak it. That would be a duplicate, that you don’t have to count twice.