SOLUTION: 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
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-> SOLUTION: 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
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Question 1140291: 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 ARRAGE THEMSELVES IF 2 AMONG THEM REFUSE TO SIT TOGETHER? Answer by ikleyn(52898) (Show Source):
1) IN HOW MANY WAYS CAN 6 INDIVIDUALS BE SEATED IN A ROUND TABLE WITH 6 CHAIRS?
In 5! = 1*2*3*4*5 = 120 ways. (The "ways" are circular permutations in this case (!) )
2) SUPPOSE 2 PERSONS WANTED TO BE SEATED SIDE BY SIDE ,IN HOW MANY WAYS CAN THEY DO IT ?
In 2*4! = 2*(1*2*3*4) = 2* 24 = 48 ways.
The factor "2" before 4! is due to the fact that there are 2 permutations of these two persons.
3) IN HOW MANY WAYS CAN THESE 6 INDIVIDUALS ARRAGE THEMSELVES IF 2 AMONG THEM REFUSE TO SIT TOGETHER?
This number is the complement of 48 to 120: in 120-48 = 72 ways.
