I found this equation on wikipedia to resolve the secretary problem. I understand it but I have a small problem.
Theoretically, if I would not want to reject any applicant, I should use $r = 0$ (edit : $r = 1$, because we reject the $r - 1$ applicants) and I would select the first applicant (because it is the best among the ones we didn't see in the rejection list) .
In this case, the probability that I choose the best applicant should be $\frac1 n$ (with $n$ the number of applicants). But in reality, the equation doesn't allow one to pick $r = 1$ because of the sum.
Is there a more generic equation to take in account this value of the number of reject applicants ?