  Using a sample of 106 million $\psi(3686)$ decays, $\psi(3686) \to \gamma
\chi_{cJ} (J = 0, 1, 2)$ and $\psi(3686) \to \gamma \chi_{cJ}, \chi_{cJ} \to
\gamma J/\psi$ $(J = 1, 2)$ events are utilized to study inclusive $\chi_{cJ}
\to$ anything, $\chi_{cJ} \to$ hadrons, and $J/\psi \to$ anything
distributions, including distributions of the number of charged tracks,
electromagnetic calorimeter showers, and $\pi^0$s, and to compare them with
distributions obtained from the BESIII Monte Carlo simulation. Information from
each Monte Carlo simulated decay event is used to construct matrices connecting
the detected distributions to the input predetection "produced" distributions.
Assuming these matrices also apply to data, they are used to predict the
analogous produced distributions of the decay events. Using these, the charged
particle multiplicities are compared with results from MARK I. Further,
comparison of the distributions of the number of photons in data with those in
Monte Carlo simulation indicates that G-parity conservation should be taken
into consideration in the simulation.
