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27 Jan 2019, 18:28
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
72% (00:53) correct
28%
(01:20)
wrong
based on 182
sessions
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Not Attempted Yet
How many different three-digit integers have exactly three different digits?
(A) 504
(B) 648
(C) 720
(D) 891
(E) 1,000
I'm wondering if the way I did it makes sense...
(A) 504
(B) 648
(C) 720
(D) 891
(E) 1,000
I'm wondering if the way I did it makes sense...
1) Ignoring the restriction that 0 can't be in the first position: 10P3 = 10*9*8 = 720
2) Remove the possibilities with 0 in the first position (1/10th the total of 10P3): 720/10 = 72
3) Subtract the possibilities with 0 in first position from total: 720 - 72 = 648
Explanation:
There are nine different possibilities for the first digit: anything between 1 and 9. The tricky part of this question is moving to the second digit. Again, there are nine possibilities for the second digit: any number between 0 and 9, not including the one using for the first digit. Remember, a three-digit number can have zero as a digit, just not as the first digit. Finally, the third digit has eight possibilities: anything between 0 and 9 except for the two digits used already. The number of possible integers, then, is: 9 × 9 × 8 = 648, choice (B).
2) Remove the possibilities with 0 in the first position (1/10th the total of 10P3): 720/10 = 72
3) Subtract the possibilities with 0 in first position from total: 720 - 72 = 648
Explanation:
There are nine different possibilities for the first digit: anything between 1 and 9. The tricky part of this question is moving to the second digit. Again, there are nine possibilities for the second digit: any number between 0 and 9, not including the one using for the first digit. Remember, a three-digit number can have zero as a digit, just not as the first digit. Finally, the third digit has eight possibilities: anything between 0 and 9 except for the two digits used already. The number of possible integers, then, is: 9 × 9 × 8 = 648, choice (B).
27 Jan 2019, 18:35
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The possibility of being a three digit integer is when we don't consider the first digit to be 0
For the second we can consider 0
Thus
9*9*8
648
For the second we can consider 0
Thus
9*9*8
648
03 Aug 2019, 01:25
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How many different three-digit integers have exactly three different digits?
(A) 504
(B) 648
(C) 720
(D) 891
(E) 1,000
Source: Math Bible (Jeff Sacksmann)
(A) 504
(B) 648
(C) 720
(D) 891
(E) 1,000
Source: Math Bible (Jeff Sacksmann)
