maybe i'm a simpleton, but i'm surprised that i'm the only one here to interpret "counting" as referring to ... counting. like, the "one, two, three" / "make a list" kind of counting.
... which is also a perfectly respectable way to solve GMAT combinatorics problems.
in fact, just making a list and counting things can often be more efficient than any formula-based method, especially when the numbers of things involved in the problem are moderate (as they almost always will be in GMAC problems).
for instance, consider #132 in the OG quant review book (can't reproduce here).
... try 4 colors (A, B, C, D):
A
B
C
D
AB
AC
AD
BC
BD
CD
it took me less than 10 seconds to make that list (... and i'm dyslexic, so, really, yeah, it's not going to take you very long.)
that's only 10 shipping codes. not enough.
... but we're done, since we can realize (without doing the work) that adding another color will clearly create more than 2 additional possibilities. so that will give us the 12 we need.
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the above is just an illustration of the use of LITERAL "counting", which i'd guess is what the original poster meant by "counting". (if it's not, then still note that it's an important technique.)
in terms of "when should i use this?" --
the best advice i can give is, "just try something." if it works, awesome! if not, just quit and try something else.
Ron has been teaching various standardized tests for 20 years.
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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