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

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(52915) (Show Source): You can put this solution on YOUR website!
.

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.

-------------------

See the lesson
- Persons sitting around a cicular table
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

RELATED QUESTIONS
IN HOW MANY WAYS CAN 6 INDIVIDUALS BE SEATED IN A ROUND TABLE WITH 6 CHAIRS? A.)... (answered by Edwin McCravy)

In how many ways can 5 people be seated in 8 chairs around a round... (answered by ikleyn)

In how many ways can 6 children be seated in a round... (answered by vleith,hibiskus)

In how many ways can 6 girls and 2 boys be seated in a circular table with boys seated to (answered by Edwin McCravy)

In how many ways can 4 girls be seated in a row of 6 chairs? (answered by ikleyn)

How many ways can 25 people be seated in a round table of there are 15 chairs? (answered by ewatrrr)

In how many ways can 8 persons be seated at a round table if a certain 2 are to sit next... (answered by ikleyn)

In how many ways can a family of 8 members be seated at a circular table with only 5... (answered by Alan3354)

In how many ways can a family of 8 members be seated at a circular table with only 5... (answered by greenestamps)