A number plate has 2 letters followed by 4 digits.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A number plate has letters followed by digits. How many plates are possible if letters and digits may repeat? How many if the letters may repeat but no digit is used twice?
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. With repetition. Each letter has ways and each digit ways: .
Step 2. No repeated digit. The letters still give ways. The digits give .
Step 3. Multiply. .
Answer: plates, and with no repeated digit.
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