Problem Solving

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?

1 36^ 6

2 36!/30!6!

3 36!/30!

4 (36!/6)!

5 30!

Shamhoon 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?

1 36^ 6

2 36!/30!6!

3 36!/30!

4 (36!/6)!

5 30!

As we have 10 digits and 26 letters , means total 36 different characters.

and license plate can have 6 characters.

Unique plates count should be 36^6.

IMO A.

Shamhoon 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?

1 36^ 6

2 36!/30!6!

3 36!/30!

4 (36!/6)!

5 30!

(0-9)=10 digits
A-Z= 26 alphabets

total options for filling the number plate=10+26=36;

for filling up the first position on the number 36 options are there, similary for 2nd also there are 36..hence total no. of ways of filling up the 6 positions are 36*36*36*36*36*36=36^6;

hence A

it should be 36^6 as each of the 6 places can be filled out in 36 ways so 36*36*36*36*36*36

however if there was a constraint that no repetition is allowed, then answer would have been 36P6 or 36*35*34*33*32*31

Guys,

the question is not complete... is it with repeatition or with out..
if we can re-use then 36 power 6 else 36*35*.....

Now let us use the question...
AAAAAA is also a unique license plate ...but
--- combination of letters and digits... 36^6 is NOT the answer
atleast 1 should be either letter or word

digits or letters: 36^6 is the answer

For these type of questions you have to ask how many things are available for each space and then consider if order is important.

here we have 6 spaces and 36 options to use. with no constraints on repetion each space has 36 options available. you multiply these together to get 36^6. Order here is important so you do not have to divide out any repeat groupings so the answer is 36^6.

Best of Luck

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?

yes actually after solving the question initially i got 36^6. although the question asks us "how many Unique license plates are there"? question still doesn't make it clear whether he is disallowing repetitions.
however the concept of linear arrangement does not specify that if the question doesn't mention repetitions then we are free to consider "with repetitions". This is something that we have started assuming for our convenience. well such a question would be too vague to answer then.

Thank you so much for the replies...

The question given is complete.

and the answer given is 36 ^ 6

but the doubt is , like some of you pointed out is that the question mentions " unique number plates "

if the number plates are unique then the numbers and/ or letters cannot be repeated. right?

Shamhoon wrote:Thank you so much for the replies...

The question given is complete.

and the answer given is 36 ^ 6

but the doubt is , like some of you pointed out is that the question mentions " unique number plates "

if the number plates are unique then the numbers and/ or letters cannot be repeated. right?

Hi Shamhoon

Your doubt is sensible.

But number plate with names line AA5544 , AAAAA3 can also be unique though there is a repetition in this.

If we have two plates with same name like AA55AA and AA55AA then they wouldn't be unique.

Hope it clarifies.