Calculate the number of combinations of 23 objects in a 5 inch square

Question

This is a design question where the objects are moved around within the space.

Answer 1

That depends on 1) how much room each object takes up 2) whether all objects must be in the box and 3) whether overlapping and/or stacking of the objects is allowed. Going with the simplest scenario of each object taking up a 1-inch square, all required to be in the box and no stacking, there are 5x5 or 25 positions available for the 23 objects and 2 empty positions. Thus, for the first such square, there are 25 possible choices, 24 for the second, 23 for the third and so forth. The total possible combinations would then be 25*24*23*... or 25 factorial.