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# Of the three-digit positive integers that have no digits

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Intern
Joined: 08 Nov 2008
Posts: 38
Of the three-digit positive integers that have no digits [#permalink]

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17 Nov 2008, 09:39
Of the three-digit positive integers that have no digits equal
to zero, how many have two digits that are equal to each
other and the remaining digit different from the other two?
A. 24
B. 36
C. 72
D. 144
E. 216

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VP
Joined: 17 Jun 2008
Posts: 1477

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17 Nov 2008, 09:54
E. 216

The numbers will be of the form aab, aba, baa where a and b are non-zero.

Hence, total number = 9*8*3
Current Student
Joined: 28 Dec 2004
Posts: 3288
Location: New York City
Schools: Wharton'11 HBS'12

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17 Nov 2008, 10:13
i get E as well..

basically you have say 11X where x is 8 possibilites, then you have 22X..33X so you have 9*8 ways when you have the first two digits the same, same thing when you have the last 2 digits the same,i.e 72 and then you have 1X1 another 72 ways..so in all you have 72*3 ways..or 216

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Re: three digit intergers   [#permalink] 17 Nov 2008, 10:13
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# Of the three-digit positive integers that have no digits

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