Let $R$ be a commutative finite ring with a unit. In this work, we focus on the number of units, zero-divisors, idempotents and nilpotents of the ring $R$. First, we do this for $R = M_n(F)$, where $F$ is a field. Since the factor ring of the ring $R$ by its Jacobson radical $J$ is a direct product of matrix rings over fields, we calculate the number of units, zero-divisors, idempotents and nilpotents of the factor ring and then infer these quantities in the ring $R$. Here we observe that the number of idempotents of the ring $R$ cannot be calculated exactly, so we find an upper bound for this number. We then calculate the number of units, zero-divisors, idempotents and nilpotents of the ring $R = M_n({\mathbb Z}_{p^t})$, where $p$ is a prime number. Finally, we do the same for the ring $R = M_n({\mathbb Z}_m)$, where $m= p_1^{t_1} \ldots p_k^{t_k}$.
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