Hello. I have a factorial study design where I need to show participants 9 out of 108 questions. Each question consists of an image (I have 108 of them) and several sliders. The images in the questions show different rooms with different furnitur
e arrangements and different flooring materials. More precisely, I have 3 different room types, 3 possible furniture arrangements, and 12 different flooring materials. I am interested in achieving the following:

1. A given participant sees 3 images of room A, 3 images of room B, and 3 images of room C.


2. All nine images contain the same furniture arrangement.


3. Each image has a different flooring material.


4. I need to balance stimuli presentation.

I don't even know how to start doing this, but I would imagine it would require naming each question with keywords that identify its room type, furniture arrangement, and floor material, and then generating a random set of numbers to pick the questions: 1 number for furniture arrangement and 9 numbers to select materials —no numbers needed for room type as all three would be shown to each participant.
Is it possible to select the questions in such a way? Is it possible to balance the question selection? I'm thinking perhaps one can access qualtrics balanced random generator, the same that the engine uses to randomize and balance questions, but that's just a guess.
In any case, any help would be greatly appreciated. Here's an image showing the different room types, and so on.