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A state issues automobile license plates that begin with two

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Retired Moderator
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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A state issues automobile license plates that begin with two [#permalink] New post 05 Aug 2018, 14:37
Expert's post
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Question Stats:

76% (00:51) correct 23% (01:08) wrong based on 93 sessions
A state issues automobile license plates that begin with two letters selected from a 26- letter alphabet, followed by four numerals selected from the digits 0 through 9, inclusive. Repeats are permitted. For example, one possible license plate combination is GF3352.

Quantity A
Quantity B
The number of possible unique license plate combinations
6,000,000


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Retired Moderator
User avatar
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3036 [0], given: 394

Re: A state issues automobile license plates that begin with two [#permalink] New post 07 Aug 2018, 06:16
Expert's post
Explanation

This is a combinatorics problem. The license plates have 2 letters followed by 4 numbers, so make 6 “slots” and determine how many possibilities there are for each slot. There are 26 letters in the alphabet and 10 digits to pick from, so:

Attachment:
Capture.PNG
Capture.PNG [ 16.87 KiB | Viewed 2769 times ]



Multiply 26 × 26 on the calculator to get 676. Add four zeros for the four 10’s to get 6,760,000. Quantity A is greater.
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Re: A state issues automobile license plates that begin with two [#permalink] New post 04 Dec 2018, 10:49
Hi,

Please clarify the following doubt - how can the license plate be unique if we repeat the alphabets /numbers? Thanks.
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Re: A state issues automobile license plates that begin with two [#permalink] New post 06 Jan 2019, 22:38
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anudec4 wrote:
Hi,

Please clarify the following doubt - how can the license plate be unique if we repeat the alphabets /numbers? Thanks.


If uniqueness of the plates was an issue, I'm pretty sure that it would be specified. But it's a good point to mention.
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Re: A state issues automobile license plates that begin with two [#permalink] New post 10 May 2020, 05:54
I did 26 *25 * 10 *9 *8*7 and didn't read properly that question explicitly mentioned repeating is allowed.
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Re: A state issues automobile license plates that begin with two [#permalink] New post 10 May 2020, 06:08
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ZIONGRE wrote:
I did 26 *25 * 10 *9 *8*7 and didn't read properly that question explicitly mentioned repeating is allowed.


If repetitions are not allowed, your calculations are perfect.
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Re: A state issues automobile license plates that begin with two   [#permalink] 10 May 2020, 06:08
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