It is equally valid (or even more valid) to state there are zero ways of choosing zero things because 'choosing' something implies there is actually something to choose. If I ask you to choose something from an empty box, you would not 'choose' something (Oh how nice of you! No let's see what will I choose... Ummmmm....Oh. I know! I'll choose... NOTHING!... Oh, it's my favorite!) but reply "Sorry, but there is nothing to choose". In a programming language this would result in a runtime error and certainly not in a number.