This talk concerns the averaging principle for a fully coupled two time-scale system, whose slow process is a diffusion process and fast process is a purely jumping process on an infinitely countable state space. The ergodicity of the fast process has important impact on the limit system and the averaging principle. We showed that under strongly ergodic condition, the limit system admits a unique solution, and the slow process converges in the L^1-norm to the limit system. However, under certain weaker ergodicity condition, the limit system admits a solution, but not necessarily unique, and the slow process can be proved to converge weakly to a solution of the limit system. Furthermore, some results on LDP of such two time-scale system are also discussed.