Five distinct flags are available: 3 small flags (Red, Green, Blue) and 2 large flags (Yellow, White). A signal is generated by hoisting either 4 flags or all 5 flags on a vertical pole. If exactly 4 flags are used, the top flag must be a large one. The total number of different signals that can be generated is

Step-by-step solution

The problem can be divided into two cases based on the number of flags used. Case 1: A signal is generated using exactly 4 flags. The top position is restricted to be a large flag. Since there are 2 large flags, the top position can be filled in 2 ways. The remaining 3 positions on the pole must be filled using any of the remaining 4 flags. This can be done in ⁴P₃ = 4 3 2 = 24 ways. Total signals using 4 flags = 2 24 = 48 . Case 2: A signal is generated using all 5 flags. There is no restriction on the top flag in