N people sit around a circular table. You have to find the probability that two particular people won't be sitting together.
Answers
Answer:
(N - 3)/(N - 1)
Step-by-step explanation:
If N people are sitting around circular table then the number of ways they can be seated i.e. the number of arrangements = (N - 1)!
If two particular people are sitting together then considering them as one person, now total number of people that are to be arranged are N - 1, they can be arranged around the circular table in (N - 1 - 1)! or (N - 2)! ways while the two persona themselves can be arranged in 2! ways.
Therefore, total arrangements when two particular people are sitting together
= (N - 2)!2!
No. of arrangements where two particular people are not sitting together
= (N - 1)! - (N - 2)!2!
= (N - 1)(N - 2)! - (N - 2)! × 2
= (N - 2)!(N - 1 - 2)
= (N - 2)!(N - 3)
Probability that two particular people are not sitting together
= (N - 2)!(N - 3)/(N - 1)!
= (N - 2)!(N - 3)/ (N - 1)(N - 2)!
= (N - 3)/(N - 1)