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A number plate is in the format of XXYYYY where X can be any

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Current Student
Joined: 11 May 2008
Posts: 552
A number plate is in the format of XXYYYY where X can be any [#permalink]

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25 Jul 2008, 03:51
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A number plate is in the format of XXYYYY where X can be any of the 26 letters and Y can be any number (0-9). How many combinations are there if the plate starts with the letter N and has at least 1 non-zero digit?
A. 26^2*10^4
B. 260,000
C. 259,974
D. 259,324
E. 259,996
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Joined: 24 Jun 2008
Posts: 1346

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25 Jul 2008, 04:18
arjtryarjtry wrote:
A number plate is in the format of XXYYYY where X can be any of the 26 letters and Y can be any number (0-9). How many combinations are there if the plate starts with the letter N and has at least 1 non-zero digit?

For the two letters we have one choice for the first letter (it must be N), and 26 choices for the second letter: 1*26 = 26 choices in total.

For the four digits, they can be any of the 10*10*10*10 = 10,000 four digit sequences except 0000. We have 9,999 choices in total.

26*9999 = 26*(10,000 - 1) = 260,000 - 26 = 259,974
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Manager
Joined: 27 May 2008
Posts: 139

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25 Jul 2008, 07:40

Here's my approach:

1*26*10^4

Now there would be 26 cases when the number plate would read something like:

NA0000, NB0000..........................NZ0000

Thus subtracting those cases from 1

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Joined: 07 Nov 2007
Posts: 1765
Location: New York

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25 Jul 2008, 10:29
IanStewart wrote:
arjtryarjtry wrote:
A number plate is in the format of XXYYYY where X can be any of the 26 letters and Y can be any number (0-9). How many combinations are there if the plate starts with the letter N and has at least 1 non-zero digit?

For the two letters we have one choice for the first letter (it must be N), and 26 choices for the second letter: 1*26 = 26 choices in total.

For the four digits, they can be any of the 10*10*10*10 = 10,000 four digit sequences except 0000. We have 9,999 choices in total.

26*9999 = 26*(10,000 - 1) = 260,000 - 26 = 259,974

agree with you .
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Manager
Joined: 14 Jun 2007
Posts: 158
Location: Vienna, Austria

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30 Jul 2008, 00:21
experts, can someone tell me why it is not:
26*26*9999

cheers
Manager
Joined: 27 May 2008
Posts: 139

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30 Jul 2008, 02:39
domleon wrote:
experts, can someone tell me why it is not:
26*26*9999

cheers

I am sure u missed on the following part:

How many combinations are there if the plate starts with the letter N and has at least 1 non-zero digit?

The first letter of the number plate is fixed as N. Thus another multiplication with 26 is not needed.
Re: combination   [#permalink] 30 Jul 2008, 02:39
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A number plate is in the format of XXYYYY where X can be any

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