What does an n-tuple actually represent? A ruler measures distances, what does a cartesian product represent? What exactly is an ordered pair consisting of a red shirt, size XL and made in China represent?
An n-tuple represents an ordered collection of data points where each data point is independent of the others. In your example, a red shirt can be of any size and can be made in any country. A size XL shirt can be of any color and made in any country. China can make shirts of any color and any size. So, each of these three data points are independent of the other data points. (You call it an ordered pair, but I am representing it as an ordered triple. It could be either, I suppose, depending on how you create it). Beyond that, I would recommend that you meditate upon the concepts before asking questions. Some things cannot be learned by listening to others, but must be understood by really internalizing the information.