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Counting: How many integers from 100 to 999 . . .

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by Brent@GMATPrepNow » Thu Jan 15, 2009 5:22 pm
How many integers from 100 to 999 are such that all three digits are all different?
(A) 504
(B) 567
(C) 648
(D) 720
(E) 729
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by dmateer25 » Thu Jan 15, 2009 5:27 pm
_ _ _

hundreds digit can be 1 thru 9: 9 possibilities
tens digit can be any digit but that used as the hundreds digit: 8 possibilities
ones digit can be any digit but those used in the hundreds place and tens place: 7 possibilities

9 x 8 x 7 = 504

A
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by Brent@GMATPrepNow » Thu Jan 15, 2009 5:39 pm
Sorry, it's not A
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by dmateer25 » Thu Jan 15, 2009 5:45 pm
Seems like i made a stupid mistake!

Let's try this again:

hundreds digit can be 1 thru 9: 9 possibilities
tens digit can be 0 thru 9 but not what the hundreds digit is: 9 possibilities
ones digit can be any digit but those used in the hundreds place and tens place: 8 possibilities

9 x 9 x 8 =648
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by Brent@GMATPrepNow » Thu Jan 15, 2009 5:45 pm
Perfectamundo!!
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