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Posted on 2011-10-21
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Last Modified: 2012-05-12
License plates in China begin with a Chinese character designating the province, followed by a letter from the set {A,....,Z}, followed by a five character alphanumeric string (using symbols from the set {A,...,Z,0,1,....9}). What is the maximum number of plates of this type for a given Chinese province. ?

I guess
26*
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Question by:mustish1
  • 9
  • 3
  • 2
  • +1
15 Comments
 
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Expert Comment

by:sdstuber
ID: 37008032
26*  ?  


what is that supposed to be?  I don't understand your guess.


In any case, this is essentially the same as your previous question.

http://www.experts-exchange.com/Other/Math_Science/Q_27409228.html
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Expert Comment

by:sdstuber
ID: 37008033
that is,  multiply the number of possible characters in each postion
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Author Comment

by:mustish1
ID: 37008040
26*3*3
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Accepted Solution

by:
Techn9cian earned 668 total points
ID: 37008070
26*35*35*35*35*35 = 1,365,568,750
26 for A-Z
35 for A-Z, 1-9
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Expert Comment

by:sdstuber
ID: 37008079
where is 3 coming from?  And why only 2 of them?  There are 5 positions.


26 is the correct for the first character.

how many characters for the second? multiply that, then how many for the third, multiply that, and so on.

Look at the previous question.  See the pattern?
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Assisted Solution

by:joelsplace
joelsplace earned 664 total points
ID: 37008085
Number of possible characters per digit raised to the power of the number of digits. 26 letters plus 10 numbers is 36 raised to the 5th power times 26 for the digit that only allows alpha characters.
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Expert Comment

by:sdstuber
ID: 37008088
Techn9cian  - no that's not correct   (your math is right, but the answer to this question is wrong)

also, it's clear I was trying to help him understand "how" to do it.

I gave the answer directly last time because he appeared to be on the right track.  In this case the attemp 26*  appears to be just a random guess.  So I'm walking through the logic
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Expert Comment

by:Techn9cian
ID: 37008092
I didn't see the 0, sorry.
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Expert Comment

by:sdstuber
ID: 37008104
mustish1

 http:#37008033  and http:#37008079 and http:#37008085  are saying the same thing.  

Does it make sense?
0
 

Author Comment

by:mustish1
ID: 37008308
set {A,...,Z,0,1,....9})
A....Z=26+0+9

it should be 36 because of zero. I may be wrong:
26*36*36*36*36*36

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Expert Comment

by:sdstuber
ID: 37008319
yes exactly!

26 for the first  
36 for each of the following 5

you simply multiply the number available for each position

or in power notation  26*36^5  same thing, just different way of writing it
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Author Comment

by:mustish1
ID: 37008332
How to convert this number into 2 raise to power ?

1572120576
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Expert Comment

by:sdstuber
ID: 37008345
that's a different question entirely
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Assisted Solution

by:sdstuber
sdstuber earned 668 total points
ID: 37008350
easiest way to approximate is simply divide by 2 until you get to 1
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Expert Comment

by:sdstuber
ID: 37008362
or you can calculate it directly with any language or calculator that has a LOG or LN function


log(1572120576) / log(2)

ln(1572120576) / ln(2)


some languages may let you specify the base of your log though

if you have one of those, try  log(2,1572120576)
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