Reset Dependent Data Validation selections without macros?

I have data validation drop down selections in Columns A and B and C, where B is dependent on the selection in A and C is dependent on B (left to right, if you will). This works very well, but I have noticed that when I change my selection in A, the previously selected items in B and C remain. Is there a way to remove the selections (to blank cells) when any item to the left is removed or changed? For instance, if the user deletes or changes their first selection in A, B and C go blank. Or when they delete or change their selection in B, C goes blank. I'm aware of a simple macro that does this, but it seems to me that there exists a formula I could enter into the data validation or list names window that will do the trick. Any ideas?