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

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arjtryarjtry
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A number plate is in the format of XXYYYY where X can be any [#permalink] A number plate is in the format of XXYYYY where X can be any   25 Jul 2008, 03:51
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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Re: A number plate is in the format of XXYYYY where X can be any [#permalink] A number plate is in the format of XXYYYY where X can be any   25 Jul 2008, 04:18
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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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Re: A number plate is in the format of XXYYYY where X can be any [#permalink] A number plate is in the format of XXYYYY where X can be any   25 Jul 2008, 07:40
C is the answer.

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

The answer is 259974
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Re: A number plate is in the format of XXYYYY where X can be any [#permalink] A number plate is in the format of XXYYYY where X can be any   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 .
C is the answer
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Re: A number plate is in the format of XXYYYY where X can be any [#permalink] A number plate is in the format of XXYYYY where X can be any   30 Jul 2008, 00:21
experts, can someone tell me why it is not:
26*26*9999


cheers
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rahulgoyal1986
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Re: A number plate is in the format of XXYYYY where X can be any [#permalink] A number plate is in the format of XXYYYY where X can be any   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.



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