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A state issues automobile license plates that begin with two
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05 Aug 2018, 14:37
05 Aug 2018, 14:37
Expert Reply
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Question Stats:
74% (00:57) correct
25% (01:08) wrong based on 139 sessions
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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.
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.
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.
Re: A state issues automobile license plates that begin with two
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07 Aug 2018, 06:16
07 Aug 2018, 06:16
Expert Reply
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:
Capture.PNG [ 16.87 KiB | Viewed 7513 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.
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 [ 16.87 KiB | Viewed 7513 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.
Re: A state issues automobile license plates that begin with two
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04 Dec 2018, 10:49
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.
Please clarify the following doubt - how can the license plate be unique if we repeat the alphabets /numbers? Thanks.
