Permutations - practice problems

A permutation is an arrangement of objects in a specific order, representing all possible ways to organize a set of items. For n distinct objects, there are n! (n factorial) permutations. When some objects are identical, the formula becomes n!/(n₁!n₂!...nₖ!) where n₁, n₂, etc. are the frequencies of repeated elements. Circular permutations, where arrangements in a circle are considered, follow different counting rules. Permutations are essential in probability theory, cryptography, and optimization problems. Students learn to calculate permutations, distinguish them from combinations, and apply them to real-world scheduling and arrangement problems.