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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.

 Nov 17, 2022
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1 - Fix one person anywhere

 

2 - Fix the Chief and his mother as a single person

 

3 - That is: 8 people - 2 (Chief + his mother) - 1 =5 singles person left

 

4 - There are: [5 singles + 1 (Chief + his mother as 1 single person)] = 6 positions

 

5 - 6! = 720 ways of sitting in the same spot x 2! [Chief and his mother can sit to the left or the right of each other]=6! x 2! =1,440 ways of sitting around the campfire.

 Nov 17, 2022

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