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In State X, all vehicle license plates have 2 letters from the 26 lett

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In State X, all vehicle license plates have 2 letters from the 26 lett  [#permalink]

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New post 16 Mar 2016, 05:37
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E

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Re: In State X, all vehicle license plates have 2 letters from the 26 lett  [#permalink]

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New post 16 Mar 2016, 09:05
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Bunuel wrote:
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


hi,

The choices give us the answer without any calculations--


3 one digits places can take 10*10*10 ways..
so answer should have three 0s in end--...000
only E is f that form
ans E..


Proper solution will be


since repetition is allowed, we can choose 2 places for digits in 26*26
3 digits places can befilled up in 10*10*10 ways
ans= 26*26*10*10*10=676000

ans E
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In State X, all vehicle license plates have 2 letters from the 26 lett  [#permalink]

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New post 17 Mar 2016, 02:05
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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Re: In State X, all vehicle license plates have 2 letters from the 26 lett  [#permalink]

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New post 10 Jun 2017, 11:57
@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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Re: In State X, all vehicle license plates have 2 letters from the 26 lett  [#permalink]

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New post 10 Jun 2017, 12:44
startjumprun wrote:
@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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Re: In State X, all vehicle license plates have 2 letters from the 26 lett  [#permalink]

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New post 11 Jun 2017, 03:04
Bunuel wrote:
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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Re: In State X, all vehicle license plates have 2 letters from the 26 lett  [#permalink]

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New post 11 Jun 2017, 04:22
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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In State X, all vehicle license plates have 2 letters from the 26 lett  [#permalink]

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New post 11 Jun 2017, 07:47
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Bunuel wrote:
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


Take the task of creating as license plate and break it into stages.

Stage 1: Select the first character
This must be a letter from the alphabet.
So, we can complete stage 1 in 26 ways

Stage 2: Select the second character
This must be a letter from the alphabet.
Also, since repetitions are allowed, we can complete stage 2 in 26 ways

Stage 3: Select the third character
This must be a digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9)
We can complete stage 3 in 10 ways

Stage 4: Select the fourth character
This must be a digit.
Since repetitions are allowed, we can complete stage 4 in 10 ways

Stage 5: Select the fifth character
This must be a digit.
Since repetitions are allowed, we can complete stage 5 in 10 ways

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus create a license plate) in (26)(26)(10)(10)(10) ways
Note, before we perform any calculations, we should recognize that (26)(26)(10)(10)(10) = (26)(26)(1000)
So, the answer must end in 000

Answer:

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: In State X, all vehicle license plates have 2 letters from the 26 lett  [#permalink]

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New post 23 Jul 2018, 18:21
Bunuel wrote:
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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Re: In State X, all vehicle license plates have 2 letters from the 26 lett   [#permalink] 23 Jul 2018, 18:21
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