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

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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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Kudos [?]: 132595 [0], given: 12326

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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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New post 06 Oct 2017, 06:51
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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New post 06 Oct 2017, 06:58
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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Re: A number plate is in the format of XXYYYY where X can be any of the 26 [#permalink]

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New post 06 Oct 2017, 16:05
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

Kudos [?]: 4 [0], given: 54

Re: A number plate is in the format of XXYYYY where X can be any of the 26   [#permalink] 06 Oct 2017, 16:05
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