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

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Manager
Joined: 15 Dec 2015
Posts: 116
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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Updated on: 24 Aug 2017, 05:28
1
9
00:00

Difficulty:

95% (hard)

Question Stats:

35% (02:07) correct 65% (02:58) wrong based on 59 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

Originally posted by DHAR on 08 Aug 2017, 11:54.
Last edited by DHAR on 24 Aug 2017, 05:28, edited 1 time in total.
Intern
Joined: 25 Jan 2013
Posts: 27
Concentration: General Management, Entrepreneurship
Re: How many positive integers less than 9999 are there in which the sum o  [#permalink]

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08 Aug 2017, 19:03
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

Manager
Joined: 12 Sep 2016
Posts: 67
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.15
Re: How many positive integers less than 9999 are there in which the sum o  [#permalink]

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09 Aug 2017, 06:09
Can an expert please post an easy way to get the solution?
Intern
Joined: 08 Aug 2017
Posts: 1
Re: How many positive integers less than 9999 are there in which the sum o  [#permalink]

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09 Aug 2017, 09:45
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

You miss:

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

Add all again: 84 ways. And it just become worst :c
Senior Manager
Joined: 02 Apr 2014
Posts: 471
GMAT 1: 700 Q50 V34
How many positive integers less than 9999 are there in which the sum o  [#permalink]

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30 Apr 2018, 11:44
2
1
This is similiar to donut problem - Distributing n donuts among m children, such that each children may receive 0 to n donuts

we use formula: (n+m-1)!/(n!(m-1)!)

similiarly here,
we imagine 6 1's => 1 1 1 1 1 1 to be distributed among 4 places (since we have less than 9999, maximum 4 digits)
so total combinations: (6 + 4 - 1)!/ (6! * 3!) = 9!/(6! 3!) = 84
How many positive integers less than 9999 are there in which the sum o &nbs [#permalink] 30 Apr 2018, 11:44
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