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How many three-digit numbers are there such that all three digits are
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04 Oct 2022, 08:07
04 Oct 2022, 08:07
Expert Reply
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Question Stats:
35% (01:00) correct
64% (00:47) wrong based on 17 sessions
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How many three-digit numbers are there such that all three digits are different and the first digit is not zero?
(A) 504
(B) 648
(C) 720
(D) 729
(E) 810
(A) 504
(B) 648
(C) 720
(D) 729
(E) 810
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GRE Math Essentials (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
Re: How many three-digit numbers are there such that all three digits are
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31 Oct 2022, 22:37
31 Oct 2022, 22:37
1
Expert Reply
The first digit cannot be 0, so there are 9 options for the first digit.
the second digit can be any number (10 possibilities) but cannot be equal to the first digit. Therefore, there are (10-1) 9 possibilities for the 2nd digit.
The third digit can be any digit (10 possibilities) but cannot be equal to the first two digits. Therefore, there are (10-2) 8 possibilities for the 3rd digit.
So there are 9 * 9 * 8 = 648 possibilities.
the second digit can be any number (10 possibilities) but cannot be equal to the first digit. Therefore, there are (10-1) 9 possibilities for the 2nd digit.
The third digit can be any digit (10 possibilities) but cannot be equal to the first two digits. Therefore, there are (10-2) 8 possibilities for the 3rd digit.
So there are 9 * 9 * 8 = 648 possibilities.
gmatclubot
Re: How many three-digit numbers are there such that all three digits are [#permalink]
31 Oct 2022, 22:37
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