Deriving physical parameters of unresolved star clusters. I. Age, mass,
  and extinction degeneracies
  Context. Stochasticity and physical parameter degeneracy problems complicate
the derivation of the parameters (age, mass, and extinction) of unresolved star
clusters when using broad-band photometry.
  Aims. We develop a method to simulate stochasticity and degeneracies, and to
investigate their influence on the accuracy of derived physical parameters.
Then we apply it to star cluster samples of M31 and M33 galaxies.
  Methods. Age, mass and extinction of observed star clusters are derived by
comparing their broad-band UBVRI integrated magnitudes to the magnitudes of a
large grid of star cluster models with fixed metallicity Z=0.008. Masses of
stars for a cluster model are randomly sampled from the initial mass function.
Models of star clusters from the model grid, which have all of their magnitudes
located within 3 observational errors from the magnitudes of the observed
cluster, are selected for the computation of its age, mass, and extinction.
  Results. In the case of the M31 galaxy, the extinction range is wide and the
age-extinction degeneracy is strong for a fraction of its clusters. Because of
a narrower extinction range, the age-extinction degeneracy is weaker for the
M33 clusters. By using artificial cluster sample, we show that age-extinction
degeneracy can be reduced significantly if the range of intrinsic extinction
within the host galaxy is narrow.
