Let A = {a, b, c, d, e, f, g, h}. Count the number of different strings that meet each of the criteria. Strings that are five letters, letters can be repeated. Strings that are five letters, letters cannot be repeated. Strings that are five letters, starts with 'a' and ends with 'h', letters cannot be repeated. Strings that are six letters, either starts with the substring 'ab' or ends with the substring 'gh' or both, letters can be repeated. Strings that contain all eight letters exactly once. Strings that contain all eight letters exactly once and contains the substring 'bag'. Strings that contain all eight letters exactly once and the letters 'a' and 'b' must be adjacent to each other such as 'feabcdgh' and 'hgdfbaec