  The existence of strange quark stars has been proposed many years ago. More
recently, the possible co-existence of a first family composed of "normal"
neutron stars with a second family of strange quark stars has been proposed as
a solution of problems related to the maximum mass and to the minimal radius of
these compact stellar objects. In this paper we study the mass distribution of
compact objects formed in binary systems and the relative fractions of quark
and neutron stars in different subpopulations. We incorporate the strange quark
star formation model provided by the two-families scenario and we perform a
large-scale population synthesis study in order to obtain the population
characteristics. In our model, below a critical gravitational mass
$M_\mathrm{max}^H- \Delta M$ only normal (hadron) neutron stars exist. Then in
the mass range $(M_\mathrm{max}^H- \Delta M) \leqslant M \leqslant
M_\mathrm{max}^H$ strange quark stars and neutron stars coexist. Finally, above
$M_\mathrm{max}^H$ all compact objects are strange quark stars. We argue that
$M_\mathrm{max}^H$ is in the range $\sim 1.5-1.6 M_\odot$. According to our
results, the main channel for strange quark star formation in binary systems is
accretion from a secondary companion on a neutron star.This opens the
possibility of having explosive GRB-like phenomena not related to supernovae
and not due to the merger of two neutron stars. The enhancement in the number
of compact objects in the co-existence mass range $(M_\mathrm{max}^H- \Delta M)
\leqslant M \leqslant M_\mathrm{max}^H$ is not very pronounced. The number of
double strange quark star's systems is rather small with only a tiny fraction
which merge within a Hubble time. This drastically limits the flux of
strangelets produced by the merger, which turns out to be compatible with all
limits stemming from Earth and lunar experiments.
