The optimal stopping rules with multiple selections of 

$m \ge 1$ objects with the objective of maximizing 

the probability of obtaining the best object are studied 

for two problems with an unknown number of objects: 

the problem  with a random number of objects, 

and the problem where the objects arrive  according to 

a homogeneous Poisson process with unknown intensity $\lambda$.  

These two problems are variation of the so-called secretary problem.  

This article introduces an easier method based on the 

one-stage look-ahead  function (defined herein) depending on $m$ 

and its recursive relation to the  number $m$, to find the optimal 

stopping rule for all $m$, without a direct  solution of equations 

suggested by a common dynamic programming approach.