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A license plate consists of a combination of 6 digits or letters. All 17 Oct 2016, 13:51
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Hi NaeemHasan,

There might be some 'regional bias' in this question (especially if you've never seen a license plate before), but a license plate is essentially just a unique 'identifier' for a vehicle. Since the prompt does NOT state that there are any restrictions on 'where' a number or letter can be placed, we have to assume that each number and each letter can appear ANYWHERE and can ALSO REPEAT.

So, the first few license plates would be...
000000
000001
000002
000003
Etc.

And the last few license plates would be...
ZZZZZZ
ZZZZZY
ZZZZZX
Etc.

In this way, each of the 6 "spots" on the license plate could hold ANY of the 36 options (the 10 digits and 26 letters) and placing a number or letter in a 'spot' has NO effect on what can be placed in the other 'spots.' This means that we have 36^6 possible license plates.

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A license plate consists of a combination of 6 digits or letters. All 26 Jan 2021, 06:23
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Bunuel
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A license plate consists of a combination of 6 digits or letters. All numbers (0-9) and all 26 letters may be used. How many unique license plates are there?

\(A. 36^6\)

\(B. \frac{36!}{30!6!}\)

\(C. \frac{36!}{30!}\)

\(D. \frac{36!}{6!}\)

\(E. 30!\)

So the plate is like: XXXXXX. Now, each X can take 10 digits + 26 letters = 36 different values (options), thus total 36^6 unique plates are possible.

Answer: A.
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How they are unique values when each value is repeating?
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A license plate consists of a combination of 6 digits or letters. All 26 Jan 2021, 06:28
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lakshya14
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A license plate consists of a combination of 6 digits or letters. All numbers (0-9) and all 26 letters may be used. How many unique license plates are there?

\(A. 36^6\)

\(B. \frac{36!}{30!6!}\)

\(C. \frac{36!}{30!}\)

\(D. \frac{36!}{6!}\)

\(E. 30!\)

So the plate is like: XXXXXX. Now, each X can take 10 digits + 26 letters = 36 different values (options), thus total 36^6 unique plates are possible.

Answer: A.

How they are unique values when each value is repeating?
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The digits in a plate can repeat but this still gives 36^6 unique plates, unique combination of 6 digits or letters in a plate.
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A license plate consists of a combination of 6 digits or letters. All 26 Jan 2021, 07:36
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If starting digit be 0, then it will be five digit/letter instead of 6 ... Am I missing something Bunuel?
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A license plate consists of a combination of 6 digits or letters. All 26 Jan 2021, 08:15
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bobnil
If starting digit be 0, then it will be five digit/letter instead of 6 ... Am I missing something Bunuel?
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We are not talking about 6-digit number, we are talking about 6-digit license plate, which can start with 0.
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A license plate consists of a combination of 6 digits or letters. All 27 Jan 2021, 18:39
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Apply the fundamental counting principle.

Since there are no restrictions, there are 36 possible choices for each spot.

36^6

Answer is A.
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A license plate consists of a combination of 6 digits or letters. All 17 Aug 2021, 21:09
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Hi,

I am having a little trouble understanding the solution 36^6. Wouldn't this mean that 2 different license plates can be exactly the same, i.e. one can be "111111" and another can also be "111111", because ways of choosing either was 36^6?

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Shivam
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A license plate consists of a combination of 6 digits or letters. All 17 Aug 2021, 22:58
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Hi Shivam,

Since the prompt does not state that there are any restrictions on 'where' a number or letter can be placed, we have to assume that each number and each letter can appear anywhere and can also be used more than once.

So, the first few license plates would be...
000000
000001
000002
000003
Etc.

And the last few license plates would be...
ZZZZZZ
ZZZZZY
ZZZZZX
Etc.

In this way, each of the 6 "spots" on the license plate could hold ANY of the 36 options (the 10 digits and 26 letters) and placing a number or letter in a 'spot' has NO effect on what can be placed in the other 'spots.' This means that we have:

(36)(36)(36)(36)(36)(36) = 36^6 possible license plates.

GMAT assassins aren't born, they're made,
Rich
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A license plate consists of a combination of 6 digits or letters. All 02 Jun 2025, 01:13
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