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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 12, 2020
 #1
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First, we can seat the journalists.  Then we seat the baristas, then the sailor.  There are 5! ways to seat the journalists, then 2! ways to seat the baristas, then 1! way to seat the sailor.  Then we divide by 8, so there are 5!*2!*1!/8 = 30 ways to seat everyone.

 Jun 12, 2020
 #2
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I already tried that response a long time ago. It was wrong. I'm confused.

trumpstinks  Jun 12, 2020
 #3
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Maybe this video will help:

https://artofproblemsolving.com/videos/counting/chapter2/192

 Jun 12, 2020

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