For a simple random sample from a population of size \(N\), the subjects are not sampled independently because of the finite size of the population.

(a) Show that the probability of being sampled for each subject is \(\frac{n}{N}\), where \(n\) is the number of subjects in the sample.

(b) If sampled sequentially, then conditioning on the first one being sampled, the probability of sampling each of the remaining subjects is \(\frac{n-1}{N-1}\).

(c) Use (a) and (b) to show that the subjects in the simple random sample are not independent.