Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

16 Dec 2012, 08:47

11

This post received KUDOS

HumptyDumpty wrote:

Could you describe how you have arrived at your answer?

Well, here's my approach:

Case I: The repeated digit is the unit's digit. So, the 1st, 2nd and 3rd digits can be selected in 9 x 9 x 8 ways, respectively. Now the 4th digit (unit's digit) can be either equal to the 1st, 2nd or 3rd digit. Thus, in all we have: 9x9x8x3

Case II: The repeated digit is the ten's digit. So, the 1st, 2nd and 4th digits can be selected in 9 x 9 x 8 ways, respectively. Now the 3rd digit (ten's digit) can be either equal to the 1st or 2nd digit. Thus, in all we have: 9x9x2x8

Case III: The repeated digit is the hundred's digit. So, the 1st, 3rd and 4th digits can be selected in 9 x 9 x 8 ways, respectively. Now the 2nd digit (hundred's digit) is equal to the 1st digit. Thus, in all we have: 9x1x9x8

In totality, we have 9x9x8(3+2+1) = 9x9x8x6 = 3888

Hope this helps.

And P.S.: If you find this helpful please hit the kudos button. It'll be my first
_________________

If this post helped you in your GMAT prep in anyway, please take a moment and hit the "Kudos" button. It'll make my day

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

28 Dec 2012, 19:18

6

This post received KUDOS

tabsang wrote:

How many 4-digit numbers can be formed by using the digits 0-9, so that the numbers contains exactly 3 distinct digits?

(A) 1944 (B) 3240 (C) 3850 (D) 3888 (E) 4216

How many ways to select 3 digits from 0-9? \(=\frac{10!}{3!7!} = 120\) How many ways to select a repeating digits? \(3\) How many ways to arrange {D1,D2,R,R}? \(=\frac{4!}{2!}=12\)

\(=120*36 = 4320\)

Now we have 0-9 that could be the first digit. We cannot allow 0 to be the first digit. We know 0-9 will occur evenly as a first digit in 4320 counts. \(=4320 - \frac{4320}{10} = 3888\)

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

16 Dec 2012, 13:57

3

This post received KUDOS

I think I agree with you.

Here’s my approach:

You have 3!=6 of possible placements of the doubled number, because you treat the four digit number with the doubling as a 3-different-digits-number without the doubling, simply ignoring the doubling (the glue method). So you can count the possible arrangements of X Y Z=3!=6, here (the 4-digits are only illustrative):

X Y Z Z or X Y Z X Z Z Y or X Z Y Z Z X Y or Y X Z Z X Z Y or Y Z X X Z Y Z or Z X Y Z X Y Z or Z Y X

The number of possible numbers made up from digits 0-9 for each of the above possibilities is 9*9*8, i.e.:

X Y Z Z: - for X – 9 digits from 1-9 as 0 would be indifferent in the first place, - for Y – 9 digits from 0-9 except for thousands digit, - for Z Z – 8 digits from 0-9 except for thousands digit and hundreads digit.

The same scheme applies to each of the 6 possible arrangements listed above, therefore: 9*9*8*6 = 3888. The answer is D.

I hope it's correct. As usual the hardest part was to bump on the idea, however schematic this problem was.
_________________

If I answered your question with this post, use the motivating power of kudos!

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

17 Dec 2012, 09:24

3

This post received KUDOS

1

This post was BOOKMARKED

HumptyDumpty wrote:

You're right, my luck, my bad. Pity, apparently I can't understand the case thorough at the moment. I'd appreciate detailed troubleshooting to the approach, if someone loves combinatorics. Kudo for you.

Well, I did dig deep into GMAT combinatorics and got really stuck into some questions. Out of the many solutions, here's one that uses your approach in principle (Sincere thanks to the expert who helped). Have a look:

Solution: Out of the 4 digits, any 2 have to be the same. Number of ways this is possible: 4C2 = 6.

Consider one case: Tens digit and units digit are the same:

Number of options for the thousands digit = 9. (Any digit 1-9) Number of options for the hundreds digit = 9. (Any digit 0-9 not yet chosen) Number of options for the tens digit = 8. (Any digit 0-9 not yet chosen) Number of options for the units digit = 1. (Must be the same as the tens digit) To combine the options above, we multiply: 9*9*8*1 = 648.

Other cases: #ways if the HUNDREDS digit and the UNITS digit are the same (9*9*8*1) #ways if the THOUSANDS digit and the UNITS digit are the same (9*9*8*1) #ways if the HUNDREDS digit and the TENS digit are the same (9*9*1*8) #ways if the THOUSANDS digit and the TENS digit are the same (9*9*1*8) #ways if the THOUSANDS digit and the HUNDREDS digit are the same (9*1*9*8)

Total #ways = 648*6 = 3888.

Sincerely hope this helps

If this brought a smile to your face, cleared the doubt clouds and made your day then a quick kudos and a big smilie is in place.

Cheers, Taz

P.S.: It feels great that I'm able to help & share in the same way that others have helped and shared with me. Cheers to gmatclub. Cheers to bb
_________________

If this post helped you in your GMAT prep in anyway, please take a moment and hit the "Kudos" button. It'll make my day

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

17 Dec 2012, 01:39

2

This post received KUDOS

HumptyDumpty wrote:

I think I agree with you.

Here’s my approach:

You have 3!=6 of possible placements of the doubled number, because you treat the four digit number with the doubling as a 3-different-digits-number without the doubling, simply ignoring the doubling (the glue method). So you can count the possible arrangements of X Y Z=3!=6, here (the 4-digits are only illustrative):

X Y Z Z or X Y Z X Z Z Y or X Z Y Z Z X Y or Y X Z Z X Z Y or Y Z X X Z Y Z or Z X Y Z X Y Z or Z Y X

The number of possible numbers made up from digits 0-9 for each of the above possibilities is 9*9*8, i.e.:

X Y Z Z: - for X – 9 digits from 1-9 as 0 would be indifferent in the first place, - for Y – 9 digits from 0-9 except for thousands digit, - for Z Z – 8 digits from 0-9 except for thousands digit and hundreads digit.

The same scheme applies to each of the 6 possible arrangements listed above, therefore: 9*9*8*6 = 3888. The answer is D.

I hope it's correct. As usual the hardest part was to bump on the idea, however schematic this problem was.

I think there is a problem here with this approach.

Try doing the same for a 5-digit number with 4 distinct digits. Using my approach, the answer is 9*9*8*7*(4+3+2+1) = 45360

If I use your approach, the answer is as follows: 4!=24 (using glue method) And 9*9*8*7 choices for the four digits. Answer in this case would be 9*9*8*7*24 = 108864

Seems to be some confusion here.
_________________

If this post helped you in your GMAT prep in anyway, please take a moment and hit the "Kudos" button. It'll make my day

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

18 Dec 2012, 00:36

1

This post received KUDOS

Ans:

there are 3 cases: 1st case The repeated digit is the unit's digit. So, the 1st, 2nd and 3rd digits can be selected in 9 x 9 x 8 ways. Now the unit's digit can be either equal to the 1st, 2nd or 3rd digit. we have: 9x9x8x3

2nd case: The repeated digit is the ten's digit. So, the 1st, 2nd and 4th digits can be selected in 9 x 9 x 8 ways, respectively. Now the ten's digit can be either equal to the 1st or 2nd digit. we have: 9x9x2x8

3rd case: The repeated digit is the hundred's digit. So, the 1st, 3rd and 4th digits can be selected in 9 x 9 x 8 ways, respectively. Now the hundred's digit is equal to the 1st digit. we have: 9x1x9x8

so total= 9x9x8(3+2+1) = 9x9x8x6 = 3888 answer is (D).
_________________

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

17 Dec 2012, 08:55

You're right, my luck, my bad. Pity, apparently I can't understand the case thorough at the moment. I'd appreciate detailed troubleshooting to the approach, if someone loves combinatorics. Kudo for you.
_________________

If I answered your question with this post, use the motivating power of kudos!

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

18 Apr 2014, 16:49

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

24 Sep 2015, 10:09

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

I got (D) in a little over 3.5 minutes and I don't even know if it's right :O

Fixing Thousand's place and starting with 1

1 1 _ _ The empty spaces can be filled in 9x8 = 72 ways. and the hundred's, ten's and unit's place can be arranged in 3! way or 6 ways. So total combination for 1 will be 72*6 = 432

Similarly we can obtain combinations for all the remaining numbers. The thousand's place can take 9 values(since 0 cannot be at thousand's place). So total number of combinations will be 432*9 =3888

Re: How many 4-digit numbers can be formed by using the digits 0 [#permalink]

Show Tags

10 Nov 2016, 08:02

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...