What is a permutation?

A permutation refers to an arrangement of objects in a specific order. This concept is crucial in various fields of mathematics, particularly in combinatorics. When we discuss permutations, we consider the order in which elements are arranged; for example, the arrangement of a set of letters or numbers conveys different meanings depending on the sequence in which they appear.

In permutations, the same items arranged differently count as distinct outcomes. For instance, the arrangements "ABC" and "CBA" are viewed as two separate permutations despite containing the same letters. This characteristic distinguishes permutations from combinations, where the order does not matter, leading to the confusion with other concepts mentioned in the options.

Understanding permutations is particularly useful when dealing with scenarios such as organizing tasks, determining seating arrangements, or any situation where the positioning of items impacts the outcome.