This paper draws inspiration from the seminal work and great book of Bharati Krishna Tirthaji and the preceding contributions and significant contributions of Kenneth Williams, Swati Dave, Marianne Fletcher, James Glover, Veronica Prudente, Virgillo Prudente and Gowri Ramachandran. This research paper or study delves and works into the intriguing intersection and connection between Vedic Mathematics and Combinatorics, with a particular focus on permutations with repetition, permutations without repetition, combinations with repetition, and combinations without repetition. The study showcases the immense potential of Vedic Mathematics sutras when applied to these combinatorial concepts and topics, systematically building on each previous idea. This paper presents and showcases the firepower of the sutras by one more than the one before, by one less than the one before, by elimination and retention on permutations with repetition, permutations without repetition, combinations with repetition, combinations and without repetitions. The sutra vertically and crosswise is also mentioned and utilized as one of the sutras that is applied in the process to extend the process presented. Using all these sutras, a fast and a more efficient manner of solving basic combinatorics problems has been found; that is, a general formula that could be used as an algorithm. In summary, this paper pioneers a symbiotic relationship between Vedic Mathematics and Combinatorics, introducing fresh perspectives and transformative techniques in solving permutations with repetition, permutations without repetition, combinations with repetition, and combinations without repetition. It empowers mathematicians, mathematics educators, and problem solvers with a powerful new mental tool, redefining the landscape of combinatorial mathematics. Keywords: statistics and probability, combinatorics, permutation, combination, repetition, vedic math