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# A number plate is in the format of XXYYYY where X can be any of the 26

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Math Expert
Joined: 02 Sep 2009
Posts: 43867
A number plate is in the format of XXYYYY where X can be any of the 26 [#permalink]

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05 Oct 2017, 23:54
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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. 6,760,000
B. 260,000
C. 259,996
D. 259,974
E. 259,324
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Aug 2009
Posts: 5660
Re: A number plate is in the format of XXYYYY where X can be any of the 26 [#permalink]

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06 Oct 2017, 05:51
Bunuel 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?

A. 6,760,000
B. 260,000
C. 259,996
D. 259,974
E. 259,324

Hi...

I believe here that the two X and 4 Y themselves can be same or different digits that is it can be said as $$X_1X_2Y_1Y_2Y_3Y_4$$ or ABCDEF where AB are alphabets and CDEF are numbers..

so number is N _ _ _ _ _ ..
$$X_!$$ can be ONLY N so 1 way
$$X_2$$ can be any of 26 digits..
all ys can be any of 10 digits
so ways = 1*26*10*10*10*10= 260,000

But exception is where all Ys are 0, so ways that is possible = 1*26*1*1*1*1=26

ans = 260000-26=259,974
D
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Re: A number plate is in the format of XXYYYY where X can be any of the 26 [#permalink]

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06 Oct 2017, 05:58
Bunuel 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?

A. 6,760,000
B. 260,000
C. 259,996
D. 259,974
E. 259,324

XXYYYY

First X is N so only 1 way possible =1
Second X can be any of the 26 alphabets = 26
All the four Y's can take up any of the 10 digits. Hence no of ways = 10*10*10*10

So total no of ways in which a number plate in the XXYYYY format can be formed = 1*26*10*10*10*10= 260,000

But it is mentioned that the number plates contain atleast one non-zero digit. Hence we need to exclude all those number plates that are of the form
NX0000 = 1*26*1*1*1*1=26

Hence total no of plates possible = 260,000-26=259,974

Option D
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Joined: 02 Feb 2016
Posts: 22
Re: A number plate is in the format of XXYYYY where X can be any of the 26 [#permalink]

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06 Oct 2017, 15:05
The plate is in the format: "N"XYYYY

There are 26 possible values for X, 10 each for Y.

Total possibilities = 26x10^4

However, all Y cannot be 0, so, illegal possibilities = 26 x 1

Possible valid plates = 260000 - 26 = 259974
Re: A number plate is in the format of XXYYYY where X can be any of the 26   [#permalink] 06 Oct 2017, 15:05
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