Theory of Computation is a core subject in Computer Science and Engineering. The abstract machines like Finite Automata, Pushdown Automata and Turing Machine these are the basis for today¿s computer. As Theory of Computation is mathematics oriented subject, for acquiring knowledge in this we need strong mathematical analysis skill. The problems presented in the prescribed book may be limited. But it is possible to create crores of problems in each abstract machine. This book focuses on the topic, construction of finite automata that accepts three unique input characters with three equal occurrences for an unordered input. As three unique input characters are used with three occurrences the total level will be 3*3=9. In each level, we will be having some states. In the first level, the number of states is 4. In the second level, it is thirteen. In the consecutive level, it will be 40, 121, 364, 1093, 3280, 9841, 29524. Totally 1680 combinations are possible with the first possible final state is 10218 and the final possible final state is 29146. This concept is a combination of the theory of computation and permutation & combinatorics.