  Extended main-sequence turnoffs (eMSTO) have been observed in the
color-magnitude diagram (CMD) of intermediate-age and young star clusters. The
origin of the eMSTO phenomenon is still highly debated. Calculations show that
the blue and faint (BF) stars in the CMD of NGC 1866 are hydrogen main sequence
(MS) + naked He star systems. The He star derives from the massive star of a
binary system. The BF stars and the red and faint MSTO stars belong to the same
stellar population. The values of $m_{F336W}$ and $m_{F336W}-m_{F814W}$ of the
BF stars are mainly determined by the masses of He stars and H-MS stars,
respectively. The behaviors of the BF stars in the CMD are well explained by
the H-MS + He-star systems. The BF stars provide a strict restriction on the
age of the stellar population. Moreover, the bimodal MS of NGC 1866 can also be
reproduced by a younger binary population. The calculations show that part of
the blue and bright (BB) MS stars of NGC 1866 are H-MS + He-star systems, H-MS
+ white dwarf systems, and merged stars in a binary scenario. The H-MS stars of
the H-MS + He-star systems for the BB stars are significantly more massive than
those of the BF stars. Once the H-MS + He-star systems and their membership in
NGC 1866 are confirmed, the extended star-formation histories and the effects
of binaries can be confirmed in the young star cluster.
