(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 $zapprox 0.5-2$ 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 $zapprox 1-2$; irregular galaxies as seen today formed by aggregation of clouds at $zapprox 0.5-1.5$. 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.
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