I'm having no trouble selecting the counties within the Basin, but I also need to select the portions of the counties only partially within the basin. I know how to select the entirety of the counties that are partially within, but I want to select only the portions that are within the basin shapefile so I can calculate the percentage of those counties that are within the MRB.
Edit for more info: Take an example that shows a selected county - the counties layer is red and part of the county selected contains a portion of the Mississippi river basin shapefile (green). Rather than select the whole county when I select by location (I've selected those that intersect the MRB shapefile, those that are wholly within it, and those only partially within it - I still get entire counties) I would like to select only the portion of each county that contains the MRB shapefile shown in green.
Furthermore, I would like to retain the borders of each county - My end goal is to extract county-level data from a raster, but only the portions of counties within the River Basin.