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# How many numbers are there between 100 and 1000 in which all digits

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CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2700
Location: India
GMAT: INSIGHT
WE: Education (Education)
How many numbers are there between 100 and 1000 in which all digits  [#permalink]

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14 Oct 2015, 20:20
3
5
00:00

Difficulty:

35% (medium)

Question Stats:

75% (01:38) correct 25% (01:20) wrong based on 103 sessions

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How many numbers are there between 100 and 1000 in which all digits are distinct.

(A) 900
(B) 648
(C) 720
(D) 252
(E) 729

Source: http://www.GMATinsight.com

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Re: How many numbers are there between 100 and 1000 in which all digits  [#permalink]

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15 Oct 2015, 03:45
1
1
GMATinsight wrote:
How many numbers are there between 100 and 1000 in which all digits are distinct.

(A) 900
(B) 648
(C) 720
(D) 252
(E) 729

Source: http://www.GMATinsight.com

We know that numbers between 100 and 1000 will be 3 digit integers.

Let the arrangement be ABC where A,B,C represent distinct digits.

We have 9 options for A (as 0 can not start a 3 digit number), 9 options again for B and 8 for C, giving a total of 9*9*8 = 648 options.

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Joined: 09 Sep 2013
Posts: 8790
Re: How many numbers are there between 100 and 1000 in which all digits  [#permalink]

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14 Jul 2018, 03:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many numbers are there between 100 and 1000 in which all digits &nbs [#permalink] 14 Jul 2018, 03:14
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