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by danjuma » Wed Oct 06, 2010 10:55 am
In a certain province, license plates consists of 6 characters. The first 3 characters are letters of the alphabet and the last 3 characters are digits from 0 to 9. If repetitions are not allowed, how many different license plates are posible?

1.260

2.26^10

3.10^26

4.6^36

5.260^3
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by Ian Stewart » Wed Oct 06, 2010 11:04 am
If those are the answer choices, then the question must say that repetitions *are* allowed; otherwise the correct answer isn't there. If repetition is allowed, you have 26 choices for the first three symbols, and 10 choices for the remaining three, so the answer is:

26*26*26*10*10*10 = 26^3 * 10^3 = 260^3

If repetition were not allowed, you'd have 26 choices for the first symbol, 25 for the second, 24 for the third, 10 for the fourth, 9 for the fifth and 8 for the sixth, and the answer would be 26*25*24*10*9*8. That isn't equal to any of the answer choices - it's clearly divisible by both 3 and 5, and none of the answer choices is divisible by both 3 and 5.
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