In this paper, we extend the definition of Boolean canalyzing functions to the canalyzing functions of multi-state case. Namely, f:Qⁿ→Q , where Q={a₁,a₂,...,a_q} . We obtain its cardinality and the cardinalities of its various subsets (They may not be disjoint). When q=2, we obtain a combinatorial identity by equating our result to the formula in [1]. For a better understanding to the magnitude, we obtain the asymptotes for all the cardinalities as either n→∞ or q→∞.