Combinatorial problems involve counting, arranging, and selecting items from a set according to specific rules. These problems are fundamental in fields like mathematics, computer science, and statistics. They often focus on finding the number of possible combinations or permutations of a given set of elements. Common examples of combinatorial problems include the binomial coefficient, which calculates the number of ways to choose items from a larger set, and the traveling salesman problem, which seeks the shortest route visiting a set of locations. Solving these problems can help optimize resources and improve decision-making processes.