Pure: Permutations and Combinations

A. Permutation Definition: A permutation is an arrangement of objects in a specific order. Explanation: When we talk about permutations, the order in which items are arranged is crucial. For example, arranging the letters 'A', 'B', 'C' as 'ABC' is different from 'ACB' or 'BAC'. It's about how many distinct sequences or orderings can be formed from a given set of objects, either by taking all of them or a subset. Think of it as: Imagine arranging books on a shelf. If you have three different books, the order you place them in matters. Placing Book A, then B, then C is a different arrangement than placing Book C, then B, then A. Real-world application: Permutations are used in creating passwords, where the order of characters is vital. They are also applied in scheduling tasks, arranging people in a line, or determining the possible finishing orders in a race. B. Factorial (n!) Definition: The factorial of a non-negative integer 'n', denoted by n!, is the product of all positive integers less than or equal to n.