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How many positive integers less than 700 have no repetition of digits?
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08 Apr 2022, 06:23
08 Apr 2022, 06:23
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50% (02:23) wrong based on 16 sessions
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How many positive integers less than 700 have no repetition of digits?
A. 511
B. 522
C. 523
D. 738
E. 739
A. 511
B. 522
C. 523
D. 738
E. 739
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Posts: 6218
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Re: How many positive integers less than 700 have no repetition of digits?
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08 Apr 2022, 06:36
08 Apr 2022, 06:36
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Carcass wrote:
How many positive integers less than 700 have no repetition of digits?
A. 511
B. 522
C. 523
D. 738
E. 739
A. 511
B. 522
C. 523
D. 738
E. 739
Important: The integers in question can be 3-digit integers, 2-digit integers, and 1-digit integers. So we should consider three cases:
Case i: 3-digit integers that are less than 700 and have no repetition of digits)
The first digit can be 1, 2, 3, 4, 5, or 6. So, there are 6 different ways to choose the first digit.
The second digit can be any of the digits from 0 to 9, EXCEPT the digit chosen for the first digit. So, there are 9 different ways to choose the second digit.
The third digit can be any digit EXCEPT the 2 digits chosen as the first and second digits. So, there are 8 different ways to choose the third digit.
Total number of 3-digit integers = (6)(9)(8) = 432
Case ii: 2-digit integers that no repetition of digits)
The first digit can be any digit other than 0. So, there are 9 different ways to choose the first digit.
The second digit can be any of the digits from 0 to 9, EXCEPT the digit chosen for the first digit. So, there are 9 different ways to choose the second digit.
Total number of 2-digit integers = (9)(9) = 81
Case iii: 1-digit integers
This can be any digit from 1 to 9
Total number of 1-digit integers = 9
TOTAL = 432 + 81 + 9 = 522
Answer: B
Re: How many positive integers less than 700 have no repetition of digits?
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18 Sep 2023, 15:24
18 Sep 2023, 15:24
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