Question; sailing ships used to send messages with signal flags flown from their masts

Question

1. Sailing ships used to send messages with signal flags flown from their masts. How many different signals are possible with a set of four distinct flags is a minimum of two flags is used for each signal? Please explain how to do this question, I don't understand what to do.

Answer 1

So you need 2, 3, or 4 flags for each signal.

With 2 flags. First flag can be chosen in 4 ways, next in 3 (as 1 has been used). So 4 x 3 = 12 ways

With 3 flags. First flag 4 ways, second 3, third 2. So 4 x 3 x 2 = 24 ways

With 4 flags, Have to use all four, so 1 way.

So in total 12 + 24 + 1 = 37 ways