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How many different 4-digit numbers

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Math Expert
Joined: 02 Aug 2009
Posts: 7991
How many different 4-digit numbers  [#permalink]

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13 Mar 2016, 05:43
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Difficulty:

25% (medium)

Question Stats:

75% (01:42) correct 25% (02:05) wrong based on 118 sessions

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How many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2?
A. 360
B. 560
C. 760
D. 840
E. 1260

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Joined: 25 Dec 2012
Posts: 116
Re: How many different 4-digit numbers  [#permalink]

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13 Mar 2016, 05:52
chetan2u wrote:
How many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2?
A. 360
B. 560
C. 760
D. 840
E. 1260

OA after 3 days

The most restrictive case. We should have a two.
No repetition. Numbers range from 1 to 8.
= 1*7*6*5 = 210 ways we can write if '2' is in the first position.
= 4*(210)
=840 ways.

Another method.

Without restriction for 8 digits- 8*7*6*5 = 1680 Ways we can write.
Without restriction for 7 digits- 7*6*5*4 = 840 Ways.

With restriction = 1680 - 840 = 840 Ways.

IMO.D.
Intern
Joined: 23 Dec 2015
Posts: 8
Re: How many different 4-digit numbers  [#permalink]

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13 Mar 2016, 07:41
chetan2u wrote:
How many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2?
A. 360
B. 560
C. 760
D. 840
E. 1260

OA after 3 days

All possibel combinations - combinations without using digit 2

(8*7*6*5) - (7*6*5*4) = 840
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Re: How many different 4-digit numbers  [#permalink]

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15 Apr 2017, 03:29
chetan2u wrote:
How many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2?
A. 360
B. 560
C. 760
D. 840
E. 1260

OA after 3 days

Let's list all possibilities and then subtract those without 2.
$$(8*7*6*5)-(7*6*5*4)$$
$$7*6*5*4=840$$

D.
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Joined: 25 Apr 2016
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Re: How many different 4-digit numbers  [#permalink]

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15 Apr 2017, 04:09
4*7p3=840 and that implies option ->D
Intern
Joined: 18 Nov 2018
Posts: 4
Re: How many different 4-digit numbers  [#permalink]

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23 Nov 2018, 15:23
the question is asking for what are some possible way to rearrange 7 numbers into 3 columns, since 2 always occupy 1 of 4 total columns,

it is permutation, not combination where the question would give you if there are 4 columns, what are some possible ways to choose 4 numbers from 1 to 8

since it is permutation, it is 7p3 for each column, 7p3 = 7! / (7-3)! = 7 * 6 * 5 = 210
now we have the permutation for each column, now, there is digit 2 which can occupy any of 4 of 4 column
so, multiply 4 withe the permutation for each column, answer = 4 * 210 = 840
Re: How many different 4-digit numbers   [#permalink] 23 Nov 2018, 15:23
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