A selection problem with cost-‘Secretary problem’ when unlimited recall is allowed

It is required to select a good candidate from among n candidates. Taking the cost of interview into consideration, an optimum number i is determined, a random sample of size i is taken and from the sample the best candidate is chosen. The probability distribution of the absolute rank r of the chosen individual is obtained. After a fundamental theory is developed, the asymptotic theories are considered when n becomes very large, for the cases of high, medium, and low cost.