BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

pemutation / combination :-)

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 17
Joined: Sun Aug 22, 2010 5:39 am
Location: Kingdom of Saudi Arabia
GMAT Score:320
by Shamhoon » Thu Mar 31, 2011 2:19 am
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!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Senior | Next Rank: 100 Posts
Posts: 65
Joined: Mon Mar 07, 2011 12:27 am
Thanked: 6 times

by 6983manish » Thu Mar 31, 2011 2:30 am
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.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 436
Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members
Thanked: 72 times

by manpsingh87 » Thu Mar 31, 2011 2:30 am
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
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 423
Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members
Location: Seattle, WA
Thanked: 86 times

by srcc25anu » Thu Mar 31, 2011 2:32 am
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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1101
Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members
Thanked: 47 times
GMAT Score:640

by HSPA » Thu Mar 31, 2011 5:54 am
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
First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 509
Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members
Location: Irvine, CA
Thanked: 199 times
GMAT Score:750

by tpr-becky » Thu Mar 31, 2011 9:03 am
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
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 582
Joined: Tue Mar 08, 2011 12:48 amFollowed by: 6 members
Thanked: 61 times
GMAT Score:740

by force5 » Thu Mar 31, 2011 2:21 pm
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.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 17
Joined: Sun Aug 22, 2010 5:39 am
Location: Kingdom of Saudi Arabia
GMAT Score:320

by Shamhoon » Sun Apr 03, 2011 8:44 am
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?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 65
Joined: Mon Mar 07, 2011 12:27 am
Thanked: 6 times

by 6983manish » Sun Apr 03, 2011 5:46 pm
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.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1