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How many positive integers less than 9999 are there in which the sum o

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Manager
Manager
User avatar
S
Joined: 15 Dec 2015
Posts: 114

Kudos [?]: 111 [0], given: 70

GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
How many positive integers less than 9999 are there in which the sum o [#permalink]

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New post 08 Aug 2017, 12:54
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Difficulty:

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Question Stats:

28% (01:34) correct 72% (02:32) wrong based on 32 sessions

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How many positive integers less than 9999 are there in which the sum of the digits equals 6?

(A) 55
(B) 60
(C) 61
(D) 84
(E) 120
[Reveal] Spoiler: OA

Last edited by DH99 on 24 Aug 2017, 06:28, edited 1 time in total.

Kudos [?]: 111 [0], given: 70

Intern
Intern
avatar
B
Joined: 25 Jan 2013
Posts: 26

Kudos [?]: 3 [0], given: 1891

Concentration: General Management, Entrepreneurship
Re: How many positive integers less than 9999 are there in which the sum o [#permalink]

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New post 08 Aug 2017, 20:03
DH99 wrote:
How many positive integers less than 9999 are there in which the sum of the digits equals 6?

(A) 55
(B) 60
(C) 61
(D) 63
(E) 120


0006 - 4!/3! ways
1500 - 4!/2! ways
2400 - 4!/2! ways
3300 - 4!/2!2! ways
2220 - 4!/3! ways
1230 - 4! ways
1113 - 4!/3! ways

Add all: 66 ways. But answer is not matching.

Kudos [?]: 3 [0], given: 1891

Manager
Manager
User avatar
B
Joined: 12 Sep 2016
Posts: 71

Kudos [?]: 12 [0], given: 796

Location: India
Schools: Kellogg '20
GMAT 1: 700 Q50 V34
GPA: 3.33
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Re: How many positive integers less than 9999 are there in which the sum o [#permalink]

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New post 09 Aug 2017, 07:09
Can an expert please post an easy way to get the solution?

Kudos [?]: 12 [0], given: 796

Intern
Intern
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Joined: 08 Aug 2017
Posts: 1

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

Re: How many positive integers less than 9999 are there in which the sum o [#permalink]

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New post 09 Aug 2017, 10:45
vs224 wrote:
DH99 wrote:
How many positive integers less than 9999 are there in which the sum of the digits equals 6?

(A) 55
(B) 60
(C) 61
(D) 63
(E) 120


0006 - 4!/3! ways
1500 - 4!/2! ways
2400 - 4!/2! ways
3300 - 4!/2!2! ways
2220 - 4!/3! ways
1230 - 4! ways
1113 - 4!/3! ways

Add all: 66 ways. But answer is not matching.


You miss:

1122 - 4!/2!2! ways
4011- 4!/2! ways

Add all again: 84 ways. And it just become worst :c

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

Re: How many positive integers less than 9999 are there in which the sum o   [#permalink] 09 Aug 2017, 10:45
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