It is very important for complicated communication networks to be well designed so that they can use their resources well, handle errors, and grow as needed.  This study shows a new way to solve network design problems using heuristic combinatorial methods based on binomial coefficients.  The suggested method is based on carefully choosing which nodes to connect in order to minimise connection costs and increase network stability. Binomial coefficients (n k)  are used carefully to create groups of possible node pairs. This makes it easier to explore different design options in an organised way. The combinatorial framework sorts and ranks possible network designs based on performance measures like degree centrality, path redundancy, and minimal spanning constraints. The algorithm uses heuristics like greedy estimate, repeated revision, and probability sampling to find its way through the very large solution space. One important new idea is to use Pascal’s Triangle and the symmetry in (n k) = (n n–k) to cut down on the amount of work that needs to be done on the computer. This study presents a method that can be used on a large scale and is based on math.