  (Abridged) A simple quantitative model is presented for the history of
galaxies to explain galaxy number counts, redshift distributions and some other
related observations. We first infer that irregular galaxies and the disks of
spiral galaxies are young, probably formed at $z\approx 0.5-2$ from a
simultaneous consideration of colours and gas content under a moderate
assumption on the star formation history. Assuming that elliptical galaxies and
bulges of spiral galaxies, both called spheroids in the discussion, had formed
early in the universe, the resulting scenario is that spiral galaxies formed as
intergalactic gas accreting onto pre-existing bulges mostly at $z\approx 1-2$;
irregular galaxies as seen today formed by aggregation of clouds at $z\approx
0.5-1.5$. Taking the formation epochs thus estimated into account, we construct
a model for the history of galaxies employing a stellar population synthesis
model. We assume that the number of galaxies does not change except that some
of them (irregulars) were newly born, and use a morphology-dependent local
luminosity function to constrain the number of galaxies. The predictions of the
model are compared with the observation of galaxy number counts and redshift
distributions for the $B$, $I$ and $K$ colour bands. It is shown that young
irregular galaxies cause the steep slope of the $B$-band counts. The fraction
of irregular galaxies increases with decreasing brightness: at $B=24$ mag, they
contribute as much as spiral galaxies. Thus, ``the faint blue galaxy problem''
is solved by invoking young galaxies. This interpretation is corroborated by a
comparison of our prediction with the morphologically-classified galaxy counts
in the $I$ band.
