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# A three-digit code for certain logs uses the digits 0, 1, 2,

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VP
Joined: 03 Apr 2007
Posts: 1339

Kudos [?]: 859 [0], given: 10

A three-digit code for certain logs uses the digits 0, 1, 2, [#permalink]

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01 Jun 2008, 09:15
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A three-digit code for certain logs uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the
following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the
second and third digits cannot both be 0 in the same code. How many different codes are
possible?
A. 144
B. 152
C. 160
D. 168
E. 176

Kudos [?]: 859 [0], given: 10

Director
Joined: 10 Sep 2007
Posts: 934

Kudos [?]: 354 [0], given: 0

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01 Jun 2008, 09:34
One set
First digit can be selected from 8 numbers (leaving 0 and 1).
Second digit can be selected from 1 numbers (0).
Third digit can be selected from 9 numbers (leaving 0).
Total Number = 8*1*9 = 72

Second set
First digit can be selected from 8 numbers (leaving 0 and 1).
Second digit can be selected from 1 numbers (1).
Third digit can be selected from 10 numbers (no restriction).
Total Number = 8*1*10 = 80

Net total = 72 + 80 = 152

Kudos [?]: 354 [0], given: 0

SVP
Joined: 28 Dec 2005
Posts: 1543

Kudos [?]: 185 [0], given: 2

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01 Jun 2008, 10:57
i said A ... i think i interpreted the question properly. I read the last restriction as meaning that the last two numbers cant be the same, i.e. they both cannot be 0 nor can they both be 1.

So i broke it down into two cases: one with the second digit is 0 , and other case when second digit is 1.

8x1x9 (9 in the last place because you cant repeat what was in the second spot). Thats 72 choices ... and then another 72 for the second case for a total of 144

Kudos [?]: 185 [0], given: 2

Director
Joined: 10 Sep 2007
Posts: 934

Kudos [?]: 354 [0], given: 0

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01 Jun 2008, 11:08
pmenon wrote:
i said A ... i think i interpreted the question properly. I read the last restriction as meaning that the last two numbers cant be the same, i.e. they both cannot be 0 nor can they both be 1.

So i broke it down into two cases: one with the second digit is 0 , and other case when second digit is 1.

8x1x9 (9 in the last place because you cant repeat what was in the second spot). Thats 72 choices ... and then another 72 for the second case for a total of 144

Question says "both be 0 in the same code" but does not say same about 1 so you cannot assume that 1 at both places is not allowed.

Kudos [?]: 354 [0], given: 0

SVP
Joined: 28 Dec 2005
Posts: 1543

Kudos [?]: 185 [0], given: 2

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01 Jun 2008, 11:12
Doh !!!

Yes, youre right ... just re-read the question again. No mention about 1s not being able to repeat. See ,this is what is going to kill me.

Kudos [?]: 185 [0], given: 2

Re: PS-Code   [#permalink] 01 Jun 2008, 11:12
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