So I am trying to select all of the block groups inside a group of counties. So I am using the select by location tool and setting my target layer as the block group and my source layer as my counties. then I am using the are within the source layer feature.
I thought that was how you did that, but it seems that it is only selecting the ones that are completly within each county. Am i just wrong here? 
This thread has been latent for a while already, but I´m going to stir it a little, since I think there is more to be said on the subject than is stated here.
I´m using the same version ArcGIS and I could´nt get the Clementini-trick posted by mapBaker to work on my system. I kept getting the same results as "intesects" (don´know why yet, mystery still to be resolved), but thats not what is asked for in the question. ArcGIS does however have a method for selecting called "have their centroid in the source layer", which should work in most cases of this particular task.
However, you could have a situation where the centroid of a block group falls outside the border of a county. In this case that particular block group won´t be selected and your selection will not be complete. When this is the case you´ll have to switch tools and hop on to QGIS, which has a solution for this problem. In this article by Heikki Vesanto you´ll find the workflow laid out. This functionality is nowadays available as a QGIS plugin, which makes the task even much more simple.
Try the Contain (Clementini) method:
This operator provides the same results as Contain unless the source feature is entirely on the boundary of the target feature, with no part of the source feature inside the target feature. In this case, using the Contain Clementini operator does not select the target feature, whereas the Contain operator does. Clementini states that a polygon's boundary is separate from its inside and outside.
I use this method and it works well for what you're doing here.
