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In State X, all vehicle license plates have 2 letters from the 26 lett
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16 Mar 2016, 05:37
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Question Stats:
78% (01:27) correct 22% (02:10) wrong based on 273 sessions
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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
Re: In State X, all vehicle license plates have 2 letters from the 26 lett
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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
_________________
In State X, all vehicle license plates have 2 letters from the 26 lett
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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
Re: In State X, all vehicle license plates have 2 letters from the 26 lett
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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.
Re: In State X, all vehicle license plates have 2 letters from the 26 lett
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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
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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
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.
In State X, all vehicle license plates have 2 letters from the 26 lett
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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
Re: In State X, all vehicle license plates have 2 letters from the 26 lett
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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.
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78% (01:27) correct 
