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ladyrenee95
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

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ladyrenee95
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


Ready4GMAT app

total possiblities;
9^2+9^3+9^4; 7371
IMO E
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