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.
[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.