Variations - practice problems

Variations, also called arrangements, count the number of ways to select and arrange k items from n items where order matters. Unlike combinations, swapping two elements creates a different variation. The number of variations is calculated as V(n,k) = n!/(n-k)! or P(n,k) in some notations. Variations without repetition mean each item can be selected only once, while variations with repetition allow items to be reused. This concept is fundamental in counting problems, probability calculations, and code-breaking scenarios. Applications include determining possible rankings, seating arrangements, and password combinations where sequence is important.