A ship has 6 flags, all of different colours…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A ship has flags, all of different colours. A signal is flags hung one below the other. How many signals can it send? How many can it send with flags, one below another?
Need a reminder? The key ideaShow
If one event can happen in ways and, after it, a second event in ways, the two together can happen in ways. With repetition, each place keeps all its choices; without repetition, each place has one choice fewer than the one before.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Two flags. The top flag has ways, the lower flag : signals.
Step 2. Three flags. signals.
Step 3. Why order counts. Red above blue and blue above red mean different things. So each order is a different signal.
Answer: signals with flags, and with flags.
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