Permutations and combinations are concepts in mathematics that deal with counting and arranging items. A permutation refers to the different ways to arrange a set of items where the order matters. For example, arranging the letters A, B, and C can result in ABC, ACB, BAC, BCA, CAB, and CBA, totaling six unique arrangements. In contrast, a combination focuses on selecting items where the order does not matter. Using the same letters A, B, and C, the combinations would be ABC, AB, AC, and BC, resulting in four unique selections. Understanding these concepts is essential in fields like statistics, probability, and combinatorics.