Combinatorial Hashing is introduced as a method for hashing secondary keys, employing chaining to handle collisions. Chaining utilizes a linked list data structure, which supports linear search. However, this approach is computationally expensive in terms of both time and space complexity. Alternatively, open addressing can be used, but it increases the average search length, leading to higher time requirements for key retrieval. To mitigate this, depth-limited search is implemented to impose a restriction on the search depth, thereby reducing search time. Among different probing techniques, random probing is more efficient than linear probing. This work proposes a variant called Left-Right Random Probing, a refined form of random probing, to effectively manage collisions. In this implementation, Combinatorial Hashing is combined with Left-Right Random Probing, leveraging a finite set of Fibonacci numbers to introduce controlled randomization. To evaluate performance, the proposed approach is compared against linear probing, quadratic probing, and Peacock hashing. Experimental results demonstrate that Combinatorial Hashing with Left-Right Random Probing outperforms these alternative methods.