Counting principles are fundamental concepts in combinatorics that help determine the number of ways to arrange or select items. The two primary principles are the Addition Principle and the Multiplication Principle. The Addition Principle states that if there are multiple ways to do something, the total number of ways is the sum of the individual options. The Multiplication Principle, on the other hand, is used when there are multiple stages or choices involved. It states that if one event can occur in m ways and a second event can occur independently in n ways, then the total number of ways both events can occur is m × n.