Hi @ethantenison and welcome. @Matthew_White has provided an overview of how to do data analysis. I believe that you are asking more about the survey design and how to show different random images to survey takers, is that right?
I would generate all of the different image permutations by some external process with your tool of choice (R, Python, etc). Then I would create many different questions with media, one for each generated image. If there are huge numbers, I'd use a script to generate the XLSForm rows.
I'd then have a single calculate with a call on once(random()) * number_of_images to select one of the images at the start of the survey. I'd use a relevant expression for each image question to only show the one that matches the provided number. That is, the first image would have a relevant expression like ${random_num} = 1, the second ${random_num} = 2, etc. That would ensure only one of the images would be shown.
Hopefully this gives you one possible general strategy. Let us know if you have additional questions.