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In State X, all vehicle license plates have 2 letters from
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07 Mar 2018, 15:25
07 Mar 2018, 15:25
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Question Stats:
80% (00:47) correct
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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
kudos to the right answer and explanation
A 23,400
B 60,840
C 67,600
D 608,400
E 676,000
kudos to the right answer and explanation
Re: In State X, all vehicle license plates have 2 letters from
[#permalink]
07 Mar 2018, 19:40
07 Mar 2018, 19:40
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Expert Reply
No math required. Almost. When we have multiple options for a series of decisions, we can multiply the number of options for each decision. In this case, the first two decisions are which letter to choose, and the last three decisions are which digit to choose. Since there are 26 letters, and 10 digits, and repetition is allowed, we can multiply as follows:
26x26x10x10x10 = ?
Advanced math students should know what 26 squared is, but we don't need to actually multiply these numbers to solve this problem. Whatever the number is, it must end in 3 zeros. Notice only one answer choice does so: E.
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26x26x10x10x10 = ?
Advanced math students should know what 26 squared is, but we don't need to actually multiply these numbers to solve this problem. Whatever the number is, it must end in 3 zeros. Notice only one answer choice does so: E.
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Re: In State X, all vehicle license plates have 2 letters from
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23 Jul 2018, 17:21
23 Jul 2018, 17:21
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Expert Reply
Carcass 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
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
_________________
In State X, all vehicle license plates have 2 letters from
[#permalink]
20 Jun 2019, 05:47
20 Jun 2019, 05:47
1
Expert Reply
Carcass 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
A 23,400
B 60,840
C 67,600
D 608,400
E 676,000
Meanwhile, in State X, in the Governor's office, the following is unfolding....
GOVERNOR: How are things going with the new license plate format?
HEAD OF SUCH THINGS: It’s going really well. We’ll be voting on a proposed format at today’s meeting.
GOVERNOR: Fantastic! How many different license plates are possible with the proposed format?
HEAD OF SUCH THINGS: 23,400
GOVERNOR: Who said what now?
So, unless we’re talking about some 51st state with only a handful of cars in it, we can safely eliminate A, B, C (just kidding)
All kidding aside, we can take the task of creating license plates and break it into stages.
Stage 1: Select the 1st character.
Since the 1st character must be a letter, we can complete stage 1 in 26 ways
Stage 2: Select the 2nd character.
Since this character must be a letter, and since we can REPEAT letters, we can complete this stage in 26 ways
Stage 3: Select the 3rd character.
Since this character must be a digit (0,1,2,3,4,5,6,7,8 or 9), we can complete this stage in 10 ways
Stage 4: Select the 4th character.
Since this character must be a digit, and since we can REPEAT digits, we can complete this stage in 10 ways
Stage 5: Select the 5th character.
Since this character must be a digit, we can complete this stage in 10 ways
By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus create a license place) in (26)(26)(10)(10)(10) ways (= 676,000 ways)
Answer: E
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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Re: In State X, all vehicle license plates have 2 letters from
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11 May 2021, 23:48
11 May 2021, 23:48
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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