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A three digit code for certain logs uses the digits 0,

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A three digit code for certain logs uses the digits 0, [#permalink] New post 05 Jul 2008, 11:45
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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 number 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
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Re: A three digit code [#permalink] New post 05 Jul 2008, 12:46
TheBigCheese wrote:
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 number 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


first digit 8 options, second and third 19 options (second digit two options, third digit - ten options, minus 0-0)-> 8*19=80+72=152 -> B
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Re: A three digit code [#permalink] New post 05 Jul 2008, 19:41
i get B-152. I considered the two cases separately; one case where 2nd digit was 0, and other case where second digit was not zero.

8x1x10 if second digit is 1

8x1x9 if second digit is 0

together you have 152
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Re: A three digit code [#permalink] New post 06 Jul 2008, 17:11
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 number 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

Let the code be XYZ
X can take 8 values-2,3,4,5,6,7,8,9
Y can take 2 values- 0,1
Z can take 9 if y = 0 or if Y = 1 then 10 values

if y = 0 :
we have 8*1*9 = 72 options

if y = 1 :
we have 8*1*10 = 80 options
Total = 72+80 = 152.

B
Re: A three digit code   [#permalink] 06 Jul 2008, 17:11
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