Sequence Counts

A permutation counts arrangements where order matters. The letters A, B, C can be arranged in 6 ways: ABC, ACB, BAC, BCA, CAB, CBA. With 4 items, you get 24 arrangements. With 10 items, you get over 3.6 million. The factorial function — written n! — drives this explosive growth.

Permutations answer a different question than combinations. "Which 3 students get awards?" is a combination. "Who gets first, second, and third prize?" is a permutation. The distinction determines whether you divide by the ordering factor or not.

Understanding this difference prevents counting errors that cascade through probability calculations, brackets, and scheduling.