1. Permutation

Definition: Arrangement of items where order matters and no repetition is allowed.

Use Case: Ranking players, assigning unique positions (e.g., gold-silver-bronze).

Formula: P(n, r) = n! / (n - r)!

1. Variation (Without Repetition)

Definition: Filling positions where order matters but values are not repeated.

Use Case: Filling seats with different people (fixed slots).

Formula: V(n, r) = n! / (n - r)!

1. Variation (With Repetition)

Definition: Filling positions where order matters and repetition is allowed.

Use Case: Setting 4-digit passcodes, choosing ice-cream scoops in order.

Formula: V(rep)(n, r) = n^r

1. Combination (Without Repetition)

Definition: Selection where order doesn’t matter and no repetition.

Use Case: Choosing a team, selecting books regardless of order.