Question

In how many ways can 8 people sit down in a row of 8 chairs? a) without any restriction b) two specific people will not sit next to each other. c) the probability that those 2 persons end up next to each other.

Answer 1

a) Total number of ways to sit = 8! = 40320

b) Number of ways where two specific people will not sit next to each other = Total number of ways to sit - Number of ways where two specific people will sit next to each other = 8! - 7! * 2 = 30240

c) P(those 2 persons end up next to each other) = Number of ways where two specific people will sit next to each other / Total number of ways to sit

                                   = 7! * 2 / 8!

                                   = 0.25