FTCE General Knowledge Math Practice Test 2026 - Free Practice Questions and Study Guide

The relationship between permutations and combinations is fundamentally rooted in the concept of order. Permutations refer to arrangements in which the order of elements matters. For example, if you are arranging the letters A, B, and C, the arrangement ABC is considered different from ACB. In this case, each arrangement represents a unique permutation because the sequence in which the letters are arranged makes a difference.

On the other hand, combinations focus on selecting items where the order does not matter. Using the same letters A, B, and C, the selection {A, B} is equivalent to {B, A} in combinations because both selections represent the same group of letters without regard to order.

Therefore, the distinction that permutations count order while combinations do not accurately summarizes their relationship. This understanding is crucial in various applications, such as statistics, probability, and problem-solving, as it affects how one calculates outcomes based on whether the arrangement or the group is of primary concern.