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# The Number of five-digit telephone numbers having atleast

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Joined: 14 Dec 2007
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The Number of five-digit telephone numbers having atleast [#permalink]  30 Dec 2007, 05:41
The Number of five-digit telephone numbers having atleast one digit repeated is ???

a) 90000 b) 100000 c) 30240 d) 69760 e) 69000

Let me explain how did I solve this problem

Total 5 digit numbers ( repetitions included) = 9*10^4 = 90000( 100000-10000)

Total no of 5 digit numbers without any repitition= 10p5-9p4= 27216( 10p5 is the total 5 digit numbers - 9p4( 5 digit numbers which have 0 in the begining))

===> Number of five-digit telephone numbers having atleast one digit repeated is == 90000 - 27216 .which is none of the answers given above.

AM I MISSING ANYTHING HERE????

CEO
Joined: 17 Nov 2007
Posts: 3577
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Kudos [?]: 2169 [0], given: 359

Re: Number of 5 digit numbers having atleast 1 digit repeate [#permalink]  30 Dec 2007, 06:14
Expert's post
D

Total number: N=10^5 (there are no restriction of 0xxxx numbers)
Total number without repeated digits: N1=10*9*8*7*6
Total number with repeated digits: N2=N-N1=10^5-10*9*8*7*6=69760
Re: Number of 5 digit numbers having atleast 1 digit repeate   [#permalink] 30 Dec 2007, 06:14
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