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

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Joined: 15 Dec 2015
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GMAT 1: 660 Q46 V35
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How many positive integers less than 9999 are there in which the sum o  [#permalink]

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New post Updated on: 24 Aug 2017, 05:28
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Difficulty:

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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.
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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 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

Add all: 66 ways. But answer is not matching.
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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, 06:09
Can an expert please post an easy way to get the solution?
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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, 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

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

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New post 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
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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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