Summarize polygon area using another polygon

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I have a shapefile representing public/private lands in Montana. This is a multipart shapefile where I've simplified attributes so that #1==private and #0==public.

Next I have a shapefile of counties for the state. How could I easily summarize the total area of public vs private by county?

Do I need to rasterize and go about it that way?

I have an ArcEditor (Standard) and Spatial Analyst license.



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