I've never known why, but problems involving circular tables are the
same as if we had the unrealistic situation where the table, chairs, 
and people were on a large revolving platform and the table, chairs,
and people rotated at different angles would not be considered 
different arrangements.  

We can choose the seating order of the English majors 3!=6 ways, the 
seating order of the anthropology majors 2!=2 ways, and the seating 
order of the history majors 5!=120 ways. 

That's (6)(2)(120)=1440 ways.

If the 3 groups were in a straight line they could be arranged in
3!=6 ways, but since the table is considered to be on a turntable, 
there are only 2!=2 ways. [They are English, anthropology, history, 
or English, history, anthropology. Any other order of the major 
subjects could be had by rotating the imaginary turntable.]

Answer: 1440*2 = 2880 ways.

Edwin