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# The digits 0 to 9 are used to form three digit codes; however, there a

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
The digits 0 to 9 are used to form three digit codes; however, there a  [#permalink]

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02 Oct 2018, 02:12
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:51) correct 23% (02:15) wrong based on 62 sessions

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The digits 0 to 9 are used to form three digit codes; however, there are a few conditions to be followed: the first digit cannot be 0 or 9, the second digit must be 0 or 9, and the second and third digits cannot both be ‘9’ in the same code. If the digits may be repeated in the same code, how many different codes are possible?

(A) 152
(B) 156
(C) 160
(D) 729
(E) 1000

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Director
Joined: 20 Feb 2015
Posts: 767
Concentration: Strategy, General Management
Re: The digits 0 to 9 are used to form three digit codes; however, there a  [#permalink]

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02 Oct 2018, 07:09
Bunuel wrote:
The digits 0 to 9 are used to form three digit codes; however, there are a few conditions to be followed: the first digit cannot be 0 or 9, the second digit must be 0 or 9, and the second and third digits cannot both be ‘9’ in the same code. If the digits may be repeated in the same code, how many different codes are possible?

(A) 152
(B) 156
(C) 160
(D) 729
(E) 1000

Case 1
take 0 as the second digit

no of ways we can select the first digit = 10-2(cannot be 0 or 9) = 8 ways
no of ways we can select second digit = 1 way ( 0 )
no of ways we can select the third digit = 10 ways
total = 8*1*10 = 80 ways

case 2
when the second digit is 9 , we have 8*1*9 = 72 ways
total 80+72 = 152 ways
A
Re: The digits 0 to 9 are used to form three digit codes; however, there a   [#permalink] 02 Oct 2018, 07:09
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