Combinatorial theorems are mathematical principles that help us count and arrange objects in specific ways. They provide formulas and methods to solve problems related to combinations, permutations, and arrangements. These theorems are essential in fields like computer science, statistics, and operations research. One well-known combinatorial theorem is Pascal's Triangle, which illustrates the coefficients of binomial expansions. Another important concept is the Pigeonhole Principle, which states that if more items are placed into fewer containers, at least one container must hold more than one item. These theorems form the foundation for more complex combinatorial problems.