  The objective of this paper is to show that the so-called unified approach to
stopping problems with unknown cardinality introduced in Bruss (1984) proves to
be efficient for solving other types of best-choice problems. We show that what
we will call the alternative-choice stopping problem, which will be exemplified
right away in Section 1, can be seen as a "two-sided" Secretary problem. This
problem is instigated by a former problem of R. R. Weber (Cambridge
University). Our approach yields for unknown cardinality the sharp lower bound
$1/2$ for the probability of success. This problem is, at the same time, a
special case of a model more generally based on $k \ge 2$ linearly ordered
subsets. We shall also give the solution for such problems for k independent
streams of arrivals. Our approach is elementary and self-contained.
