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How many different three-digit integers have exactly three different

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Manager
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Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 65
How many different three-digit integers have exactly three different  [#permalink]

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New post 27 Jan 2019, 17:28
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

64% (01:34) correct 36% (01:17) wrong based on 16 sessions

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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

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).
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Re: How many different three-digit integers have exactly three different  [#permalink]

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New post 27 Jan 2019, 17:35
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
GMAT Club Bot
Re: How many different three-digit integers have exactly three different   [#permalink] 27 Jan 2019, 17:35
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