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

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

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New post 26 Mar 2015, 04:29
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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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Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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New post 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.



answer B

\(9*9*8\)
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Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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New post 27 Mar 2015, 08:39
2
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.
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Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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New post 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
3digitnumbers_text.PNG [ 9.62 KiB | Viewed 13444 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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New post 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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Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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New post 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
correct answer - B
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Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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New post 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.
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Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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New post 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
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Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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New post 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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Re: How many three-digit numbers are there such that all three digits are  [#permalink]

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New post 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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Re: How many three-digit numbers are there such that all three digits are   [#permalink] 03 Jan 2019, 11:50
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