In many cases we can use combinatorial methods, e.g., the coefficient method and the Riordan arrays etc., to prove combinatorial identities. In this paper, by making use of some unusual techniques, we achieve some specific combinatorial identities. Specifically, we derive some new identities involving two kinds of Stirling numbers, reciprocal of binomial coefficient, harmonic numbers, Bell numbers and the number of derangements, by utilizing given probability expressions, properties of mathematical expectation, binomial identities and polynomial identities.