Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 2"

(red the problem wrong, I thought it was talking about the answer. :embarrased:)
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==Solution==
 
==Solution==
Since the digits must be in increasing order, they must all be non-zero. We choose 7 digits out of 9, and when we do, they have only one order, so we choose them regardless of order, or <math>\binom{9}{7}=\binom{9}{9-7}=\dfrac{9\cdot 8}{2}=\boxed{036}</math>.
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{{solution}}
  
 
==See also==
 
==See also==
  
 
[[Category:Intermediate Combinatorics Problems]]
 
[[Category:Intermediate Combinatorics Problems]]

Revision as of 19:50, 19 June 2008

Problem

Let $N$ denote the number of $7$ digit positive integers have the property that their digits are in increasing order. Determine the remainder obtained when $N$ is divided by $1000$. (Repeated digits are allowed.)

Solution

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See also