The most basic ideas in combinatorics include: factorials The number of possible arrangements of distinct items is n-factorial, written , which equals * Example: Three items, A, B, and C, can be arranged in different ways: ABC, ACB, BAC, BCA, CAB, and CBA. permutations The number of arrangements that are possible when a subset of items is taken from a set of distinct items is a "permutation of objects taken at a time", which can be written as or , and is equal to . * Example: The number of possible arrangements of the four letters A, B, C, D, taken two at a time, is : AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, and DC. combinations The number of possible subsets of items taken from a set of items, where the order of the items doesn't matter (e.g., the sets ABC a