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# How many different positive integers can be formed

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Manager
Joined: 23 Sep 2013
Posts: 130
Concentration: Strategy, Marketing
WE: Engineering (Computer Software)
How many different positive integers can be formed  [#permalink]

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24 Feb 2015, 11:42
7
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:20) correct 45% (02:17) wrong based on 87 sessions

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How many different positive integers can be formed using each digit in the set {0,1,3,3,3,7,8} exactly once?(Naturally, the number can't begin with 0)
A. 160
B. 720
C. 1440
D. 4320
E. 5040

Please provide explanation for the choice you mark as correct.

-------------------------------------
Kudos is a nice way to say thanks !
Manager
Joined: 21 Aug 2014
Posts: 152
Location: United States
Concentration: Other, Operations
GMAT 1: 700 Q47 V40
GMAT 2: 690 Q44 V40
WE: Science (Pharmaceuticals and Biotech)
Re: How many different positive integers can be formed  [#permalink]

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24 Feb 2015, 12:07
1
solitaryreaper wrote:
How many different positive integers can be formed using each digit in the set {0,1,3,3,3,7,8} exactly once?(Naturally, the number can't begin with 0)
A. 160
B. 720
C. 1440
D. 4320
E. 5040

Please provide explanation for the choice you mark as correct.

-------------------------------------
Kudos is a nice way to say thanks !

Since the first number can't be 0, then there are only 6 possible numbers than there could be. Then the following 6 number are a regular permutation, with 3 of the elements being the same

Number of integers will be 6*6!/3!= 720

Hope it is clear,
Nacho
Manager
Joined: 21 Aug 2014
Posts: 152
Location: United States
Concentration: Other, Operations
GMAT 1: 700 Q47 V40
GMAT 2: 690 Q44 V40
WE: Science (Pharmaceuticals and Biotech)
How many different positive integers can be formed  [#permalink]

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24 Feb 2015, 12:07
solitaryreaper wrote:
How many different positive integers can be formed using each digit in the set {0,1,3,3,3,7,8} exactly once?(Naturally, the number can't begin with 0)
A. 160
B. 720
C. 1440
D. 4320
E. 5040

Please provide explanation for the choice you mark as correct.

-------------------------------------
Kudos is a nice way to say thanks !

Since the first number can't be 0, then there are only 6 possible numbers that we could use in that possition. Then the following 6 number are a regular permutation, with 3 of the elements being the same

Number of integers will be 6*6!/3!= 720

Hope it is clear,
Nacho
Current Student
Joined: 18 Oct 2014
Posts: 801
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: How many different positive integers can be formed  [#permalink]

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27 Jul 2016, 13:37
solitaryreaper wrote:
How many different positive integers can be formed using each digit in the set {0,1,3,3,3,7,8} exactly once?(Naturally, the number can't begin with 0)
A. 160
B. 720
C. 1440
D. 4320
E. 5040

Please provide explanation for the choice you mark as correct.

-------------------------------------
Kudos is a nice way to say thanks !

First digit can take 6 values= 1,3,3,3,7,8
second digit can take 6 values= 5 remaining from the above set + 0
3rd digit can take 5 values and so on

6*6*5*4*3*2 are the total ways when numbers are allowed to repeat.

But since 3 is three times, divide the above expression by 3!

6*6*5*4*3*2/3!= 720

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Manager
Joined: 29 May 2016
Posts: 93
Re: How many different positive integers can be formed  [#permalink]

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28 Jul 2016, 01:08
can we say 7!/ 3! = 840 = total numbers
and keeping 0 a first location then 6!/3! = 120 would be the number when 0 at first locatio
840 -120 = 720
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Joined: 09 Sep 2013
Posts: 13316
Re: How many different positive integers can be formed  [#permalink]

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06 Aug 2018, 02:46
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Re: How many different positive integers can be formed   [#permalink] 06 Aug 2018, 02:46
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