In how many ways can 12 people sit around a table so that all shall not have the same neighbours in any two arrangements?
Answers
Answer:
11 ! /2 ways
Step-by-step explanation:
12 people can be sit around a table in (12 – 1)! = 11 !
but each person will have the same neighbors in clockwise and anticlockwise arrangements
so the required number would be = 11 ! /2 = 19,958,400
in 11 ! /2 ways 12 people can sit around a table so that all shall not have the same neighbors in any two arrangements
Required number of ways is 19958400.
Step-by-step explanation:
First of all, there are two conditions needed to be satisfied!
Condition I,
12 People to be seated around a Table
Condition II,
No same neighbors to seated next to or
Each person should have the same neighbors in clockwise or anticlockwise arrangements
As per I-Condition, 12 People can be seated around a Table = (12 - 1)!
= 11!
As per II-Condition, there are only TWO arrangements = 11! / 2
= (11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / 2
= 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3
= 19,958,400
So, The Required Number of Ways is 19958400.