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A tribe of eight villagers sits in a circle around a campfire. If the chief must sit beside his mother, how many different seating arrangements are possible? Two seating arrangements are considered the same if each individual has the same person to the right and the same person to the left in both.

 Dec 27, 2022
 #1
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[8 - 1] ! ==7 - fixed one in any position

 

Of the 7 remaining people, take the Chief and his mother as one person.

 

So, we have: 6! ==720 ways - but the Chief and his mother can sit to left or right of each other.

 

Therefore, we have: 6! x 2! ==1,440 ways of sitting around a camp fire.

 Dec 27, 2022
 #2
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Let's have the mother sit first. It doesn't matter where she sits cuz it's the same when rotated. Now let's seat the Chief. He has 2 spaces. Next, 6 people can be placed anywhere, so it is 6!=6*5*4*3*2*1*2=1440

 Dec 27, 2022

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