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Bunuel
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Two alphabets, 3 digits.
Ways of selecting 3 digits = 10X10X10 = 1000
Ways of selecting two alphabets = 26X26
In total total ways of selecting 5 vaccancies = 676000

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@bunuel....please help me....According to me theanswer should have been 26 x 26 x 10 x 10 x 9
The reason being the number plate cant end with 000. and hence to make sure that the last number is not 0, I multiplied it with 9.

Please let me know if my reasoning is flawed.
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@bunuel....please help me....According to me theanswer should have been 26 x 26 x 10 x 10 x 9
The reason being the number plate cant end with 000. and hence to make sure that the last number is not 0, I multiplied it with 9.

Please let me know if my reasoning is flawed.

The question implies that it can actually end with 000, nothing in the stem hints otherwise. See it says: "repetition of letters and numbers is allowed".
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Bunuel
In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?

A. 23,400
B. 60,840
C. 67,600
D. 608,400
E. 676,000

Since the letters and digits can be repeated. The required combination will be 26x26x10x10x10 = 676000
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Thanks a lot Bunuel

I got confused thing that number plate like AA000 will not make sense. But there is no need to think so much when Q clearly state what is to be done. Thanks again.
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Bunuel
In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?

A. 23,400
B. 60,840
C. 67,600
D. 608,400
E. 676,000

The number of possible license plates is 26 x 26 x 10 x 10 x 10 = 676,000.

Answer: E
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26 * 26 * 10 * 10 * 10
=<something>000 (the number will definitely end with 000)
only choice E has such a number, so I am not even going to try multiplying the first two 26

Answer: E
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