  A version of the classical secretary problem is studied, in which one is
interested in selecting one of the b best out of a group of n differently
ranked persons who are presented one by one in a random order. It is assumed
that b is a preassigned (natural) number. It is known, already for a long time,
that for the optimal policy one needs to compute b position thresholds, for
instance via backwards induction. In this paper we study approximate policies,
that use just a single or a double position threshold, albeit in conjunction
with a level rank. We give exact and asymptotic (as n tends to infinity)
results, which show that the double-level policy is an extremely accurate
approximation.
