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# How many three-digit integers can be created from 5 distinct digits?

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
How many three-digit integers can be created from 5 distinct digits?  [#permalink]

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09 Oct 2018, 00:49
00:00

Difficulty:

15% (low)

Question Stats:

72% (00:43) correct 28% (00:35) wrong based on 64 sessions

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How many three-digit integers can be created from 5 distinct digits?

A) 10

B) 15

C) 20

D) 30

E) 60

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Manager
Joined: 10 Jan 2013
Posts: 172
Location: India
Concentration: General Management, Strategy
GMAT 1: 600 Q43 V30
GPA: 3.95
Re: How many three-digit integers can be created from 5 distinct digits?  [#permalink]

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09 Oct 2018, 02:08
Bunuel wrote:
How many three-digit integers can be created from 5 distinct digits?

A) 10

B) 15

C) 20

D) 30

E) 60

My approach:

pick 3 digits from 5 digits ---> 5 C 3 = 10

and arranging 3 digits in 3! ways = 6

so total = 6*10 = 60
Manager
Joined: 21 Jun 2017
Posts: 234
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: How many three-digit integers can be created from 5 distinct digits?  [#permalink]

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10 Oct 2018, 20:45
What if a zero gets placed on the first position ?
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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: How many three-digit integers can be created from 5 distinct digits?  [#permalink]

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10 Oct 2018, 20:55
1
ShankSouljaBoi wrote:
What if a zero gets placed on the first position ?

In this case a number is no longer a five-digit, it becomes four digit number.
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Joined: 29 Oct 2012
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Re: How many three-digit integers can be created from 5 distinct digits?  [#permalink]

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10 Oct 2018, 22:46
1
let's denote each digit of an integer with 1,2,3

1 can be filled in 5 ways
2 in 4
3 in 3

so distinct numbers= 5*4*3=60

p.s. question should mention 5 distinct digits doesn't have 0 in it. else the answer should change to 4*4*3=48, since 023 will be a 2 digit number and not 3 so 1 can be filled in only 4 ways.
Re: How many three-digit integers can be created from 5 distinct digits?   [#permalink] 10 Oct 2018, 22:46
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