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The solution of the secretary problem is of course only meaningful if it is justified to assume that the applicants have no knowledge of the decision strategy employed, because early applicants have no chance at all and may not show up otherwise.
There are also numerous other assumptions involved in the problem that restrict its applicability in modelling real employment decisions. For one, it is rarely the case that hiring the second-best applicant is as bad as hiring the worst. For another, it is also probably rare that interviewing
One important drawback for applications of the solution of the classical secretary problem is that the number of applicants <math> n </math> must be known in advance which is rarely the case. One way to overcome this problem is to suppose that the number of applicants is a random variable <math>N </math> with a known distribution of <math>P(N=k)_{k=1,2,\cdots} </math> (Presman and Sonin, 1972). For this model, the optimal solution is in general much harder, however. Moreover, the optimal success probability is now no longer around 1/''e'' but typically lower. Indeed, it is intuitive that there should be a price to pay for not knowing the number of applicants. However, in this model the price is high. Depending on the choice of the distribution of <math>N</math>, the optimal win probability may even approach zero. Looking for ways to cope with this new problem led to a new model yielding the so-called 1/e-law of best choice.
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