Question 1194447: IN HOW MANY WAYS CAN 6 INDIVIDUALS BE SEATED IN A ROUND TABLE WITH
6 CHAIRS?
A.) SUPPOSE 2 PERSONS WANTED TO BE SEATED SIDE BY SIDE ,IN HOW MANY
WAYS CAN THEY DO IT?
B.) IN HOW MANY WAYS CAN THESE 6 INDIVIDUALS ARRANGE THEMSELVES IF
2 AMONG THEM REFUSE TO SIT TOGETHER?
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website! IN HOW MANY WAYS CAN 6 INDIVIDUALS BE SEATED IN A ROUND TABLE
WITH 6 CHAIRS?
The table and chairs are all resting on a huge lazy Susan.
If it weren't on a huge lazy Susan, the answer would be 6!,
but since we can turn the huge lazy Susan so that any one of
the 6 can face north, we must divide by 6, making it 5! = 120
ways.
A.) SUPPOSE 2 PERSONS WANTED TO BE SEATED SIDE BY SIDE ,IN HOW
MANY WAYS CAN THEY DO IT?
They can be seated together in 2 ways. Then there are 4 single
people and one pair of people. That would be 5! if the table
weren't on a lazy susan. So we must divide by 5. So the answer
is (2)(4!) = 24.
B.) IN HOW MANY WAYS CAN THESE 6 INDIVIDUALS ARRANGE THEMSELVES
IF 2 AMONG THEM REFUSE TO SIT TOGETHER?
We subtract the 24 from the 120. 120-24 = 96 ways.
Edwin
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