How many different license plates can fit this description? A_ _ and three digits which contains 1 and 2

  • #26
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Part kidding, more pedantic. Maybe useful.

The problem does not say anything about what letter set is expected. It is an assumption made by we as problem solvers that all letters of the alphabet are valid. It's a fair assumption, but an assumption nonetheless.
But the problem does specify a context (license plates) - one in which a non-conventional letter set is specified.


It's the kind of thing that could earn the student bonus marks for pointing out ( definitely in addition to providing the expected answer!)
Yea I already got what you mean. Thanks for the explanation again. Forgive me if you got me wrong :)
 
  • #27
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Half kidding, half pedantic. Maybe useful.

The problem does not say anything about what letter set is expected. It is an assumption made by we as problem solvers that all letters of the alphabet are valid. It's a fair assumption, but an assumption nonetheless.
There's a context, as you note below. Although I don't believe the OP is a native speaker of English, the problem is written in English, so it's reasonable to assume that the Roman alphabet is the one in play, with its 26 upper-case characters. That's a reasonable assumption, but IMO it is not reasonable to assume that, say, some letters or letter combinations aren't allowed, or that digits are anything other than the decimal digits 0 through 9.
If the person who wrote the problem wanted to add restrictions on certain letters or combinations thereof, he or she should have included them.

But the problem does specify a context - one in which a non-conventional letter set is specified.
How so?
Here is the problem statement from post #1:
A witness to a hit-and-run accident tells the police that the license plate of the car in the accident, which contains three letters followed by three digits, starts with the letter A and contains both the digits 1 and 2. How many different license plates can fit this description?
Which non-conventional letter set do you believe is specified here?
 
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  • #28
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If the person who wrote the problem wanted to add restrictions on certain letters or combinations thereof, he or she should have included them.
I couldn't agree more :ok:
 
  • #29
DaveC426913
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Although I don't believe the OP is a native speaker of English?
I would not have thought that. It was not my intention to obfuscate - only to elaborate.

How so?
Here is the problem statement from post #1:
Which non-conventional letter set do you believe is specified here?
The set used for license plates, of course. i.e.: 26, sans I, O and Q.
 
  • #30
kuruman
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I would not have thought that. It was not my intention to obfuscate - only to elaborate.
The set used for license plates, of course. i.e.: 26, sans I, O and Q.
Just to be difficult, the witness could have seen a made-to-order vanity license plate "AQT 812" on a pizza delivery vehicle. Note that it contains "Q" and fits the parameters of the problem.

A cutie ate one too.
 
  • #31
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The set used for license plates, of course. i.e.: 26, sans I, O and Q.
That was an additional assumption/restriction on your part, not one that was given in the problem statement, and one that likely would have led to an incorrect answer.
 
  • #32
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While that's probably outside the scope of the question
Yes.
mentioning it, and providing a second solution - might net you bonus marks!
Or not...
But the problem does specify a context (license plates) - one in which a non-conventional letter set is specified.
No, there is no mention whatsoever in the problem statement (which I quoted several posts back) about any non-conventional letter sets or any restrictions other than three letters followed by three digits.

Since the original question has been answered to the OP's satisfaction, and further talk about reduced sets of letters is off-topic, I am closing this thread.
 
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  • #33
haruspex
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Of course I can, here below;
View attachment 263365
I hope our answers are the same 😅
You are double counting some of the numerics. E.g. you are counting 112 as an example of x12 and as an example of 1x2.
 
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  • #34
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You are double counting some of the numerics. E.g. you are counting 112 as an example of x12 and as an example of 1x2.
So the answer became 36.504
 
  • #36
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Yes.
I guess there is no a similar application at letters order.
 
  • #37
haruspex
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I guess there is no a similar application at letters order.
Quite so, that was easier. Had you only been told there was at least one A then, depending on your approach, there would have been a risk of double counting.
(But in that specific case the easy way is 263-253.)
 
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