It is shown that the number of non-void arrangementsof {1, …k}, whereis some realization of a random variableXwith distributiondefined by,which occur in connection with the rencontre problem (as the probability formfixed points of permutations of {1, … ,n} selected with probability), is the uniquely determined unbiased estimator of. Herestands for the one-point mass at zero. Furthermore, the class of all unbiased estimators ofnwith respect to the family, where the casen= 0 is excluded, is determined and all locally MVU estimators at everyin the modelare characterized. In particular, it turns out that there does not exist a uniformly MVU resp. a locally MVU estimator fornat everyin the model.