A code has 1, 2 or 3 letters, each from A, B, C, D and E.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A code has , or letters, each from A, B, C, D and E. Letters may repeat. How many codes are there?
Need a reminder? The key ideaShow
If a task can be done in ways or in other ways, with no way in both, it can be done in ways. Stages one after another multiply; separate cases add. Fill a place that has a rule first.
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. The cases. A code has exactly one length, so the cases do not overlap.
Step 2. Count each. , then , then .
Step 3. Add. codes.
Answer: codes.
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