  A double exchange model for degenerate $e_g$ orbitals with intra- and
inter-orbital interactions has been studied for the electron doped manganites
A$_{1-x}$B$_{x}$MnO$_3$ ($x > 0.5$). We show that such a model reproduces the
observed phase diagram and orbital ordering in the intermediate bandwidth
regime and the Jahn-Teller effect, considered to be crucial for the region
$x<0.5$, does not play a major role in this region. Brink and Khomskii have
already pointed this out and stressed the relevance of the anistropic hopping
across the degenerate $e_g$ orbitals in the infinite Hund's coupling limit.
  From a more realistic calculation with finite Hund's coupling, we show that
inclusion of interactions stabilizes the C-phase, the antiferromagnetic
metallic A-phase moves closer to $x=0.5$ while the ferromagnetic phase shrinks.
This is in agreement with the recent observations of Kajimoto et. al. and
Akimoto et. al.
