Several generalizations and variations of Chu-Vandermonde identity

In this paper we prove some combinatorial identities which can be considered as generaliza-tions and variations of remarkable Chu-Vandermonde identity. These identities are proved by using an elementary combinatorial-probabilistic approach to the expressions for the k-th moments (k = 1, 2) of some particular cases of investigated discrete random variables by the author of this paper [16]. As applications of one of these Chu-Vandermonde-type identities, we prove two congruences modulo p4 and modulo p5, where p ? 5 is a prime number.