A permutation is an ordered arrangement. If order matters, it is a permutation. The number of ways to arrange n distinct objects is n!. For 3 objects, there are 6 permutations: ABC, ACB, BAC, BCA, CAB, CBA.

When choosing r objects from n and arranging them, the count is n! / (n − r)!, written P(n, r) or nPr. For example, the number of ways to award gold and silver medals to 8 runners is P(8, 2) = 56. Order matters because gold and silver are different.

Permutations appear in probability, cryptography, and scheduling. They are distinct from combinations, where order does not matter. Understanding the difference is essential in combinatorics. The formulas are simple, but applying them correctly requires care.

• Ordered arrangement of objects
• n objects have n! permutations
• P(n, r) = n! / (n − r)!
• Order matters, unlike combinations