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# How many three-digit numbers are there such that all three digits are

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Math Expert
Joined: 02 Sep 2009
Posts: 57238
How many three-digit numbers are there such that all three digits are  [#permalink]

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26 Mar 2015, 04:29
00:00

Difficulty:

15% (low)

Question Stats:

74% (01:00) correct 26% (01:32) wrong based on 254 sessions

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How many three-digit numbers are there such that all three digits are different and the first digit is not zero?

A. 504
B. 648
C. 720
D. 729
E. 810

Kudos for a correct solution.

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Director
Joined: 07 Aug 2011
Posts: 511
GMAT 1: 630 Q49 V27
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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26 Mar 2015, 06:12
Bunuel wrote:
How many three-digit numbers are there such that all three digits are different and the first digit is not zero?

A. 504
B. 648
C. 720
D. 729
E. 810

Kudos for a correct solution.

$$9*9*8$$
Intern
Joined: 13 Jan 2015
Posts: 13
GMAT 1: 750 Q50 V41
GPA: 3.86
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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27 Mar 2015, 08:39
3
The first digit cannot be 0, so there are 9 options for the first digit.
the second digit can be any number (10 possibilities) but cannot be equal to the first digit. Therefore, there are (10-1) 9 possibilities for the 2nd digit.
The third digit can be any digit (10 possibilities) but cannot be equal to the first two digits. Therefore, there are (10-2) 8 possibilities for the 3rd digit.

So there are 9 * 9 * 8 = 648 possibilities.
Math Expert
Joined: 02 Sep 2009
Posts: 57238
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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30 Mar 2015, 04:00
Bunuel wrote:
How many three-digit numbers are there such that all three digits are different and the first digit is not zero?

A. 504
B. 648
C. 720
D. 729
E. 810

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

3digitnumbers_text.PNG [ 9.62 KiB | Viewed 14922 times ]

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Joined: 06 Nov 2014
Posts: 1877
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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31 Mar 2015, 12:19
Bunuel wrote:
How many three-digit numbers are there such that all three digits are different and the first digit is not zero?

A. 504
B. 648
C. 720
D. 729
E. 810

Kudos for a correct solution.

All three digits are different and first digit is not zero.
So first digit can be filled in 9 ways.
And, second digit can be filled in 9 ways.
And, third digit can be filled in 8 ways.

Total ways = 9*9*8
= 648

Hence option (B).

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Senior Manager
Joined: 24 Nov 2015
Posts: 495
Location: United States (LA)
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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18 Apr 2016, 15:18
hundreds digit can be placed in 9 ways
tens digit can be placed in 9 ways
units digit can be placed in 8 ways
total ways = 9*9*8 = 648 ways
Manager
Joined: 18 Jun 2017
Posts: 58
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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09 Aug 2017, 01:00
From arrangement concept we can have 9 combinations [Hundred's position]* 9 [Ten's position] * 8[Unit's position]
Option B.
Intern
Joined: 13 Jul 2017
Posts: 29
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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24 Aug 2017, 07:00
for left most digit we can use any digit except zero so
1 digit:9
2nd digit:9(Since now we can use 0 but couldnot used digit we used for hundreth place)
3rd digit:8(cannot use the digit we already used for ten and hundred)
9*9*8
648
option B
Intern
Joined: 05 Apr 2018
Posts: 2
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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10 Jul 2018, 21:56
Hi Bunuel.
If the question didn't specify "first digit is non-zero", will it make any difference to the answer? I don't think it will. But wanted to confirm.

Thanks,
Apoorva
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Joined: 27 Oct 2018
Posts: 554
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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03 Jan 2019, 11:50
apoorvasharma13 wrote:
Hi Bunuel.
If the question didn't specify "first digit is non-zero", will it make any difference to the answer? I don't think it will. But wanted to confirm.

Thanks,
Apoorva

Greetings apoorvasharma13

sure won't make a difference.
it can be even confusing for who don't know whether the first digit is the first from the right or the first from the left.

(note: try tagging names to get the attention of specific user)
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Thanks for KUDOS
Manager
Joined: 27 Mar 2017
Posts: 57
Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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09 Aug 2019, 13:14
Mahmoudfawzy83 wrote:
apoorvasharma13 wrote:
Hi Bunuel.
If the question didn't specify "first digit is non-zero", will it make any difference to the answer? I don't think it will. But wanted to confirm.

Thanks,
Apoorva

Greetings apoorvasharma13

sure won't make a difference.
it can be even confusing for who don't know whether the first digit is the first from the right or the first from the left.

(note: try tagging names to get the attention of specific user)

Will it not become 10x9x8 ?
Re: How many three-digit numbers are there such that all three digits are   [#permalink] 09 Aug 2019, 13:14
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