There is an unfortunate problem with calling entropy a measure of disorder or randomness.

There is an unfortunate problem with calling entropy a measure of
disorder or randomness.  One tends to think of entropy in terms of
shuffling cards.  As a matter of fact, that's usually how it is
presented.  However, there's something missing in that picture.
What's missing is energy.

A more real picture of the way entropy works is to think of two systems
sharing energy.  If you count the number of ways that the systems may
share energy, the most probable configurations are the ones you'll see
most frequently; the less probable ones will be ones you see less
frequently.  The entropy maximizes at the most probable state.  If you
look at real systems, they follow a particular trajectory through phase
space.  If the systems are such that the details of the interactions are
not very important, but the statistics and dynamics are important, then
the distributions of the observed macroscopic variables can be written
directly in terms of the entropy (Omega(E) = exp(S(E)/k), where k =
Boltzman's constant).  In a sense, entropy is just a way to count up the
number of ways or frequencies of being able to observe a system in some
state given that its sharing energy with other systems.  (Slight
oversimplification, but not a bad starting point.)  Those energies with
large frequencies of observation are more 'random' than those with small
frequencies.  There's more ways for a bunch of molecules to fill a room
than for them to pile up into a corner; the most probable states often
look more random.  However, as the Urey (sp?) experiments demonstrate,
it is a mistake to simply assume that the second law implies that
systems move from more complicated to less complicated (a particular
interpretation of 'random' that has little to do with the actual
definition of entropy) states.