Twelve persons are arranged round the table. Find the total number of arrangements in which two particular persons amongst them are not to be side by side.
Answers
Answer:
9.10!
Step-by-step explanation:
Hi,
Let us say the two particular persons be A and B.
Total number of arrangements in which two particular persons amongst
them are not to be side by side = Total number of ways of arranging 12
persons - Total number of ways of arranging 12 persons in which A and B
sit side by side.
Total number of ways of arranging 12 persons round the table = (12 -1)!
= 11! ways
Total number of ways of arranging 12 persons in which A and B sit side by
side = Let us consider both A and B together as one and find the number
of ways which is (11-1)! but A and B can interchange among themselves
which could be done in 2 ways, hence total ways would be 2*10!.
Total number of arrangements in which two particular persons amongst
them are not to be side by side = 11! - 2.10!
= 10!(11 - 2)
= 9.10!
Hope, it helps !