Pretz
Bunuel
gmatpapa wrote:
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.366
B.36!30!6!
C.36!30!
D.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.
The question stem says "unique combinations" only. So doesn't that mean there shouldn't be repetition of the digits or alphabets? How are we authenticating the uniqueness in this problem? Could you please explain?
Using My approach, answer was:
36!/30!
Hi
Pretz,
When the question talks about unique license plates, it means that any two license plates should not be having the exact same order of characters. Uniqueness here does not mean that the characters within the license plate number should be different.
For example a license plate having the number 112233 would be different from 221133 and both are acceptable license plate numbers as there is no constraints on repetition of characters.
In cases where the characters also have to be unique within the license plate, the question prompt would give you a constraint that the characters can't be repeated.
In this case as each place on the license plate can take 36 values and there are 6 such places, there would be a total of \(36^6\) unique license plates.
Hope it's clear

Regards
Harsh