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Five journalists, two baristas, and a sailor are to be seated around a circular table. How many different arrangements are possible if the journalists must all sit together (in five consecutive seats) and the baristas must sit next to each other? (Two seatings are considered equivalent if one seating can be obtained from rotating the other.)

 Jun 27, 2020
 #1
avatar+37 
+2

There are 5! ways to put 5 journalists around the table and 2! ways to put 2 baristas around the table. Then there are ONLY 2 ways to put the sailor because the two ends are considered the same, it's just flipping another arrangement. So now we multiply 5! · 2! · 2=120 · 2 · 2=480 different arrangements.

 

Hope this helps!

 Jun 27, 2020
 #2
avatar+111626 
+1

There is only 2 ways.  That is if all the journalists are considered identical and both the  baristas are also identical.

 

If all the people are treated as individuals then there are 5! ways to set the journalists and 2 ways to seat the baristas = 5!*2 so far

then places to put the sailor.

so that is    5!*2*2 = 480 ways

 Jun 27, 2020

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