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How many four-digit numbers have at least one digit repeating?

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Manager
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Joined: 17 Jan 2017
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How many four-digit numbers have at least one digit repeating?  [#permalink]

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New post 11 May 2018, 13:14
8
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A
B
C
D
E

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  55% (hard)

Question Stats:

62% (02:14) correct 38% (01:39) wrong based on 94 sessions

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How many four-digit numbers have at least one digit repeating?
A. 3000
B. 4464
C. 4500
D. 4536
E. 5000

Source: ExpertsGlobal
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Director
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Joined: 02 Oct 2017
Posts: 727
Re: How many four-digit numbers have at least one digit repeating?  [#permalink]

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New post 11 May 2018, 15:21
2
4
Total no of 4 digit numbers- number of 4 digit when no digit repeat

Total Number of 4 digit number=9000 (from 1000-9999)

No digit repeat in 4 digit number=9*9*8*7(first 9 as zero can't come in thousand place as it will no longer be 4 digit number
One digit has already choosen for thousand place so 9 digit choice left for hundred place

Similarly 8 and 7 for ten and unit place

=9000-9*9*8*7
=4464

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Senior Manager
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Joined: 29 Dec 2017
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Concentration: Marketing, Technology
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GMAT 2: 690 Q47 V37
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WE: Marketing (Telecommunications)
Re: How many four-digit numbers have at least one digit repeating?  [#permalink]

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New post 11 May 2018, 21:35
1
push12345 wrote:

=9000-9*9*8*7
=4464



Everething is perfect, but I would add a shortcut to save some time:

9*9*8*7 = 81*56 = ....6
9000 - ....6= .....4

The only one option with 4 as a unit digit is 4464. Answer (B)
Senior Manager
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Re: How many four-digit numbers have at least one digit repeating?  [#permalink]

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New post 23 Jan 2019, 16:52
push12345 wrote:
Total no of 4 digit numbers- number of 4 digit when no digit repeat

Total Number of 4 digit number=9000 (from 1000-9999)

No digit repeat in 4 digit number=9*9*8*7(first 9 as zero can't come in thousand place as it will no longer be 4 digit number
One digit has already choosen for thousand place so 9 digit choice left for hundred place

Similarly 8 and 7 for ten and unit place

=9000-9*9*8*7
=4464

Give kudos for answer

Posted from my mobile device


Hello!

Could someone please explain to me how are we being sure that one number is going to repeat?

THank you in advance!
Intern
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Joined: 05 Jan 2019
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Re: How many four-digit numbers have at least one digit repeating?  [#permalink]

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New post 25 Jan 2019, 14:18
Hello,

Sorry, I am unclear with this part - "No digit repeat in 4 digit number=9*9*8*7...."
Can someone please explain the same?

Thanks in advance.
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Re: How many four-digit numbers have at least one digit repeating?   [#permalink] 25 Jan 2019, 14:18
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