Three flags, each of a distinct color, are used in a military drill to create different signaling codes by waving: I. A single flag of any color II. Any two flags in a specific order III. All three flags in various sequences What is the maximum number of unique codes that can be formed?

Explanation

Consider the three flags as Red (R), Blue (B), and Green (G). For condition I, using a single flag, there are 3 possible signals: R, B, G. For condition II, waving any two flags in order, the number of permutations is 3P2 = 6 (e.g., RB, BR, RG, GR, BG, GB). For condition III, using all three flags in sequence, the permutations are 3! = 6 (e.g., RBG, RGB, BRG, BGR, GRB, GBR). Adding these together: 3 (single flags) + 6 (two-flag sequences) + 6 (three-flag sequences) = 15 unique codes.