Question 1067291: A group of 3 English majors, 2 anthropology majors, and 5 history majors are going out to dinner, where they will sit at a circular table.
If students with the same major need to sit together, how many different ways can the students be seated around the table?
There are __[blank]__ different ways the students can be seated around the table.
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
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
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