Thankfully, the 3 piece box does not mean that you can send in 3 photos!
For each box, pictures, slides, and negatives are counted in groups of 25. Therefore, each "piece" is good for 25 photos. Each group of 25 frames in a negative is one piece.
For the 3 piece box, you could send in 75 photo items. For the 40 piece box, 1000 photo items. You can also always mix and match photo items in with your tapes, film reels, and audio items!