The principle of inclusion-exclusion is a counting technique used in combinatorics to calculate the size of the union of multiple sets. It accounts for overlapping elements by including the sizes of individual sets and then subtracting the sizes of their intersections. This ensures that elements counted multiple times are only counted once. For example, if we have three sets, A, B, and C, the principle states that the size of the union can be found using the formula: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|. This method is essential in various fields, including probability, statistics, and computer science.