  We explore the recently discovered solution of the driven Tavis-Cummings
model (DTCM). It describes interaction of arbitrary number of two-level systems
with a bosonic mode that has linearly time-dependent frequency. We derive
compact and tractable expressions for transition probabilities in terms of the
well known special functions. In the new form, our formulas are suitable for
fast numerical calculations and analytical approximations. As an application,
we obtain the semiclassical limit of the exact solution and compare it to prior
approximations. We also reveal connection between DTCM and $q$-deformed
binomial statistics.
