Which mathematical theory deals with the arrangement, combination, and permutation of elements?

Combinatorics is the branch of mathematics that specifically focuses on the arrangement, combination, and permutation of elements within a defined set. It explores various counting techniques and principles that allow mathematicians to determine how many different ways items can be selected or arranged. This includes concepts such as combinations, which involve selecting items without regard to the order, and permutations, which consider the arrangement in order.

The relevance of combinatorics spans various fields, including computer science, network theory, and probability, making it essential for solving problems related to counting and discrete structures. In contrast, calculus primarily deals with continuous functions and rates of change, algebra focuses on the manipulation of symbols and equations, and statistics is concerned with data analysis and interpretation rather than the arrangements of elements. Thus, combinatorics is distinctly positioned as the correct answer within the context of the question.