Andy Martin has computed the number of ways all 254 Texas counties
can be completed (as 254 factorial) -

13140590921305800461383000485312999772637584563104865500301097585436112937395030474531867208340248291212865890660793264493829608374597066104814480522325766324749346393433958125653725607028102944055895649073546925669455844464559611898118678402279915384891280928014302570181589617808257025252685647489863012884041863014084857184237663384079934731712702738308949431076917947473700246530360714416499720082234418835880264436811011656620579173171200000000000000000000000000000000000000000000000000000000000000

To compute this yourself (or almost any other giant-sized factorial) 
follow Andy's instructions.

1. Install Ruby on your PC
2. Launch irb
3. Define the factorial expression

   irb> def fact n
        total = 1
         (1..n).each{|i| total = total * i}
          return total
        end

4. Run the program -

   irb> fact 254

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Adam Helman notes this value is FAR more than the number of elementary particles 
in the known Universe. Hence multiple Texas completions will be required of
every county highpointer as there are significantly fewer of them compared to
atoms and their constituents.