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At a meeting, five scientists, two mathematicians, five journalists, two biologists, and three politicians are to be seated around a circular table.  How many different arrangements are possible if the scientists must all sit together (in five consecutive seats).  (Two seatings are considered equivalent if one seating can be obtained from rotating the other.)

Mar 25, 2023

#1
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You have 17 people.

Seat one biologist at the head of table. That leaves 16 people. 5 of them are scientists who want to sit together. We will consider them as 1 person. So, we have:16 - 5 + 1=12 people who can be seated in:

12! ways. But, the 5 scientists can rearrange themselves in 5! ways. So, the total seating of all 17 people should be: 12!  x  5! =57,480,192,000 ways of seating 17 people.

Mar 25, 2023
#2
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The best possible answer is 17. If the biologist and others are seated Ina table so we group them as one and the answer is 5. So 5 multiplied by the number of people= 85multiplied by 2= 170 so there are 170 different ways to rearrange them

Mar 25, 2023