parsimony

[flint]

I recently had a test in Ornithology and one of the questions was about determining shared derived traits, derived traits shared due to convergence, and traits shared due to common ancestry. Rather than give us a phylogeny to use we were given the combinations of traits of 5 species. There were 4 traits used and each was either derived (noted by a ' ) or ancestral. It was something like this, but I do not remember exactly the combination of traits:

The number is the species, the letters are the traits that correspond to that species.

as stated a ' denotes that the trait is derived, for example
a = ancestral
a' = derived

1: a, b, c, d'
2: a, b, c', d'
3: a', b', c, d
4: a', b', c, d (3 and 4 had the exact same combination)
5: a, b', c', d'

As I said before, I do not remember the exact combinations of traits for each species. However, I do remember this - there were either 3 ancestral and 2 derived states for each trait, or 2 ancestral and 3 derived (3 as and 2 a's, 2ds and 3d's). Doesn't that mean you can create multiple phylogenies that are equally parsimonious depending on which traits you decided to start things off with, which would therefore created different answers depending on how you created the phylogeny?