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# How many integers between 3000 and 4000 that have distinct

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Intern
Joined: 03 Aug 2013
Posts: 15

Kudos [?]: 41 [2], given: 46

How many integers between 3000 and 4000 that have distinct [#permalink]

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05 Sep 2013, 22:58
2
KUDOS
6
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Difficulty:

75% (hard)

Question Stats:

53% (01:43) correct 47% (02:06) wrong based on 146 sessions

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How many integers between 3000 and 4000 that have distinct digits and increase from left to right ?

(A) 20
(B) 48
(C) 60
(D) 120
(E) 600

My answer doesn't match with the OA so BUNUEL, NARENN, VERTITASKARISHMA, ZARRALOU, I am calling for your help
[Reveal] Spoiler: OA

Kudos [?]: 41 [2], given: 46

Intern
Joined: 31 Jan 2013
Posts: 17

Kudos [?]: 56 [2], given: 18

Schools: ISB '15
WE: Consulting (Energy and Utilities)
Re: How many integers between 3000 & 4000 having distinct digits [#permalink]

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05 Sep 2013, 23:54
2
KUDOS
Since the numbers must be distinct and increasing from left to right,

The only arrangements we could come-up with are:

345_ --> 4
346_ --> 3
347_ --> 2
348_ --> 1
356_ --> 3
357_ --> 2
358_ --> 1
367_ --> 2
368_ --> 1
378_ --> 1

Number of integers =
[Reveal] Spoiler:
20

/SW

Kudos [?]: 56 [2], given: 18

Intern
Joined: 13 Jan 2013
Posts: 5

Kudos [?]: 13 [8], given: 2

Re: How many integers between 3000 and 4000 that have distinct [#permalink]

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06 Sep 2013, 15:52
8
KUDOS
You have 0 1 2 3 4 5 6 7 8 9; So eliminate 0 1 2 3; Remain S = {4, 5, 6, 7, 8, 9} (6 digits)
Because you need 3 distinct digits which increase from left to right, take 3 digits from S.
With 3 digits which increase from left to right : only one way to arrange; Ex: 468 (not 486)
It means: 6C3 = 6!/[3!x(6 - 3)!] = 6!/[3!x3!] = 4 x 5 x 6 / 3! = 4 x 5 = 20.

Kudos [?]: 13 [8], given: 2

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16534

Kudos [?]: 274 [0], given: 0

Re: How many integers between 3000 and 4000 that have distinct [#permalink]

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24 Sep 2015, 00:35
Hello from the GMAT Club BumpBot!

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Kudos [?]: 274 [0], given: 0

Senior Manager
Joined: 18 Jun 2016
Posts: 267

Kudos [?]: 179 [0], given: 102

Location: India
Concentration: Strategy, Entrepreneurship
Schools: Olin '19 (A)
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 3.7
WE: General Management (Other)
Re: How many integers between 3000 and 4000 that have distinct [#permalink]

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09 Sep 2016, 03:49
dngboy89nh wrote:
You have 0 1 2 3 4 5 6 7 8 9; So eliminate 0 1 2 3; Remain S = {4, 5, 6, 7, 8, 9} (6 digits)
Because you need 3 distinct digits which increase from left to right, take 3 digits from S.
With 3 digits which increase from left to right : only one way to arrange; Ex: 468 (not 486)
It means: 6C3 = 6!/[3!x(6 - 3)!] = 6!/[3!x3!] = 4 x 5 x 6 / 3! = 4 x 5 = 20.

For those who could not understand why we using Combination Formula here:

We have to pick 3 different digits from the Set S = {4, 5, 6, 7, 8, 9}

We are using Combination because we are only selecting the digits as there is only 1 way to arrange them i.e. increasing order.
_________________

I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

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Rest of the Notes coming soon.

Kudos [?]: 179 [0], given: 102

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16534

Kudos [?]: 274 [0], given: 0

Re: How many integers between 3000 and 4000 that have distinct [#permalink]

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10 Sep 2017, 23:59
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).

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Kudos [?]: 274 [0], given: 0

Re: How many integers between 3000 and 4000 that have distinct   [#permalink] 10 Sep 2017, 23:59
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