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A three-digit code for certain locks 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?

Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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20 Oct 2015, 03:55

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The first digit can be filled in 8 ways For second digit , it can either be 0 or 1 Case 1 - If second digit is 1 ,Third digit can take 10 values number of codes = 8 * 1 * 10 = 80

Case 2 - If second digit is 0,Third digit can take 9 values ( Third digit can't be zero) number of codes = 8 * 1 * 9= 72

Total number of codes = 152

Answer B
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A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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20 Oct 2015, 04:19

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Bunuel wrote:

A three-digit code for certain locks 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 for a correct solution.

Total digits = 10

Code digits = X Y Z

Now Slot X can take 8 values except 0 & 1

Slot Y can take 1 value, either 0 or 1

Then, if Slot Y takes digit "0" then slot Z can only take 9 digits (It can't take digit zero)

If slot Y takes digit "1" then slot Z can take all digits i.e, all 10 digits.

Therefore possible different codes are = 8*1*9+8*1*10 = 72+80=152 Option B _________________

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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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20 Oct 2015, 06:28

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Bunuel wrote:

A three-digit code for certain locks 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 for a correct solution.

Split it up in 2 scenarios:

First scenario, second digit = 1: 8*1*10 = 80 (The first digit has 8 possible numbers, the second is one and the last can be any number since the second is one) Second scenario, second digit = 0: 8*1*9 = 72 (The first digit has again 8 possible numbers, the second is 0 in this case and therefore the last can only have 9 other digits)

Since this is an "OR" relationship, add the two 80+72 = 152

Answer B
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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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20 Oct 2015, 22:14

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Bunuel wrote:

A three-digit code for certain locks 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 for a correct solution.

we have two cases here

case 1 when 2nd digit is 0, then we can have 9 different digits in third place and 8 different digits on 1st place

no of possibilities = 9 * 8 = 72

case 2 when 2nd digit is 1, then we can have 10 different digits in third place and 8 different digits on 1st place

A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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08 Nov 2015, 08:17

Result is difference of all possible choices, minus the choices where second digit is 0 and third digit is 0.

1)All choices

On the first place you can have 8 different digits. on second you can have 2 digits and on the third you can have 10 digits. So, 8*2*10=160

2)Second and third places are 0

On the first place you can still have 8 different digits, on the second you can have only one possible coice (0) and on the third you again have only one possible choice (0). So, 8*1*1=8

A three-digit code for certain locks 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 for a correct solution.

1. Number of possibilities for the first digit is 8 2. Case 1 is when the second digit is 0, number of possibilities for the third digit is 9, for a total of 8*9 3. Case 2 is when second digit is 1, number of possibilities for the third digit is 10, for a total of 8*10 4. Total number of possibilities is (2) + (3) =152
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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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12 Sep 2017, 02:48

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A three-digit code for certain locks 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?

Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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12 Sep 2017, 03:24

First place can take 8 digits, second digit can take 2 digits(0,1) and third place can take any of the digits. 2 cases possible : Case 1 : When zero is present in second place - 8*1*9 = 72 Case 2 : When 1 is present in second place - 8*1*10 = 80

Total = 152

Option B

gmatclubot

Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5,
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12 Sep 2017, 03:24