Automatically Generating Data in Drop-Down Lists

We'll start with a little background. I have some cells in my spreadsheet that are reserved for drop-down lists (all the same list for each cell). What I am trying to do is program the cells in such a way that once a particular selection is made from the DDL in one of the cells, the cell that is three cells to the right automatically generates a different selection from that cell's DDL. Does anyone have an idea as to how I could accomplish this? Thanks.