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:)
Line 3: Line 3:
  
 
==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>.
+
{{solution}}
  
 
==See also==
 
==See also==
  
 
[[Category:Intermediate Combinatorics Problems]]
 
[[Category:Intermediate Combinatorics Problems]]

Revision as of 18:50, 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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also