rishianand7 wrote:A license plate consists of a combination of 6 digits or letters. All number 0-9 and all 26 letters may be used. How many unique license plate are there?
A) 36^6
B) 36!/30!*6!
C) 36!/30!
D) (36!/6)!
E) 30!
NOTE: I'm assuming that the license plate ABC123 is different from A1B23C, even though they use the same characters.
Take the task of building a license plate and break it into stages.
Stage 1: Select a character for the 1st position.
There are 36 characters to choose from (26 letters + 10 digits)
So, we can accomplish this stage in
36 ways.
Stage 2: Select a character for the 2nd position.
Since there is no restriction that prohibits duplicate characters, we can accomplish this stage in
36 ways.
Stage 3: Select a character for the 3rd position.
Since there is no restriction that prohibits duplicate characters, we can accomplish this stage in
36 ways.
Stage 4: Select a character for the 4th position.
We can accomplish this stage in
36 ways
Stage 5: Select a character for the 5th position.
We can accomplish this stage in
36 ways
Stage 6: Select a character for the 6th position.
We can accomplish this stage in
36 ways
By the Fundamental Counting Principle (FCP) we can complete all 6 stages (and thus build a licensne plate) in
(36)(36)(36)(36)(36)(36) ways ([spoiler]= 36^6 ways = A[/spoiler])
Cheers,
Brent
Aside: For more information about the FCP, we have a free video on the subject:
https://www.gmatprepnow.com/module/gmat-counting?id=775
