From a group of \(J\) employees, \(K\) will be selected, at

[swerve]

From a group of \(J\) employees, \(K\) will be selected, at random, to sit in a line of \(K\) chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating - both are entirely random. What is the probability that the employee Lisa has seated exactly next to employee Phillip?

1) \(K = 15\)
2) \(K = J\)

The OA is C

Source: Magoosh

[Ian Stewart]

Using only Statement 1, we might be picking only from 15 employees in total, in which case it's not likely, but also not nearly impossible, that Lisa and Philip sit together. But we might be picking from 15,000,000 employees in total, and the probability might be almost zero that we even pick Lisa or Philip to sit down, let alone that they are seated together. Using only Statement 2, it might be true that Lisa and Philip are the only two employees (K = J = 2), and it might be absolutely certain they sit together, or we might have more than 2 employees in which case the probability will be less than 1 that they sit together. But once we use both statements, we know all our numbers, so of course we can answer any question.