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Each item sold at a market is labelled with a 2-, 3-, or 4- digit code

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ladyrenee95
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Each item sold at a market is labelled with a 2-, 3-, or 4- digit code [#permalink] New post   09 Nov 2017, 18:19
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Each item sold at a market is labelled with a 2-, 3-, or 4- digit code where each digit is selected from the digits 1 through 9, inclusive. If the digits may be repeated and if the same digits used in a different order represent a different code, how many different items at the market can be labeled with a unique code?


A. 216
B. 504
C. 3,024
D. 3,600
E. 7,371


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E
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chetan2u
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Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code [#permalink] New post   09 Nov 2017, 19:35
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ladyrenee95 wrote:
Each item sold at a market is labelled with a 2-, 3-, or 4- digit code where each digit is selected from the digits 1 through 9, inclusive. If the digits may be repeated and if the same digits used in a different order represent a different code, how many different items at the market can be labeled with a unique code?


A. 216
B. 504
C. 3,024
D. 3,600
E. 7,371


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2-digit code = 9*9
3-digit code = 9*9*9
4-digit code = 9*9*9*9

total = \(9*9+9*9*9+9*9*9*9=9*9(1+9+9*9)=81*(1+9+81)=81*91\)

no more calculations required ..
UNIT's digit will be 1*1=1 and only choice with units digit as 1 is E
ans E
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Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code [#permalink] New post   09 Nov 2017, 23:19
9∗9+9∗9∗9+9∗9∗9∗9=9∗9(1+9+9∗9)=81∗(1+9+81)=81∗91

answer should be E , the only answer has last digit 1
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Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code [#permalink] New post   14 Nov 2017, 07:20
Expert Reply
ladyrenee95 wrote:
Each item sold at a market is labelled with a 2-, 3-, or 4- digit code where each digit is selected from the digits 1 through 9, inclusive. If the digits may be repeated and if the same digits used in a different order represent a different code, how many different items at the market can be labeled with a unique code?


A. 216
B. 504
C. 3,024
D. 3,600
E. 7,371


The number of 2-digit codes is 9 x 9 = 9^2, the number of 3-digit codes is 9 x 9 x 9 = 9^3, and the number of 4-digit codes is 9 x 9 x 9 x 9 = 9^4, so the total number of codes is:

9^2 + 9^3 + 9^4 = 9^2(1 + 9 + 9^2) = 81(91) = 7371

Answer: E
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Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code [#permalink] New post   11 May 2019, 08:28
ladyrenee95 wrote:
Each item sold at a market is labelled with a 2-, 3-, or 4- digit code where each digit is selected from the digits 1 through 9, inclusive. If the digits may be repeated and if the same digits used in a different order represent a different code, how many different items at the market can be labeled with a unique code?


A. 216
B. 504
C. 3,024
D. 3,600
E. 7,371


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total possiblities;
9^2+9^3+9^4; 7371
IMO E
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Lobna12
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Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code [#permalink] New post   16 May 2019, 14:43
I understand your solutions, thanks for the effort. Was wondering why cant we use permutation here?? 9P2 + 9P3 + 9P4?? Any help??
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Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code [#permalink]
16 May 2019, 14:43
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